diff --git a/src/proto_016_PtMumbai/lib_delegate/baking_actions.ml b/src/proto_016_PtMumbai/lib_delegate/baking_actions.ml
index 2b796d36b4075cbfede56cad1f5deb74e66cd825..56f56616c1518cb5a86cd02fc7bf9ba59241b6f8 100644
--- a/src/proto_016_PtMumbai/lib_delegate/baking_actions.ml
+++ b/src/proto_016_PtMumbai/lib_delegate/baking_actions.ml
@@ -126,14 +126,13 @@ type action =
   | Inject_block of {block_to_bake : block_to_bake; updated_state : state}
   | Inject_preendorsements of {
       preendorsements : (consensus_key_and_delegate * consensus_content) list;
-      updated_state : state;
     }
   | Inject_endorsements of {
       endorsements : (consensus_key_and_delegate * consensus_content) list;
-      updated_state : state;
     }
   | Update_to_level of level_update
   | Synchronize_round of round_update
+  | Watch_proposal
 
 and level_update = {
   new_level_proposal : proposal;
@@ -158,6 +157,7 @@ let pp_action fmt = function
   | Inject_endorsements _ -> Format.fprintf fmt "inject endorsements"
   | Update_to_level _ -> Format.fprintf fmt "update to level"
   | Synchronize_round _ -> Format.fprintf fmt "synchronize round"
+  | Watch_proposal -> Format.fprintf fmt "watch proposal"
 
 let generate_seed_nonce_hash config delegate level =
   if level.Level.expected_commitment then
@@ -340,8 +340,7 @@ let inject_block ~state_recorder state block_to_bake ~updated_state =
     emit block_injected (bh, signed_block_header.shell.level, round, delegate))
   >>= fun () -> return updated_state
 
-let inject_preendorsements ~state_recorder state ~preendorsements ~updated_state
-    =
+let inject_preendorsements state ~preendorsements =
   let cctxt = state.global_state.cctxt in
   let chain_id = state.global_state.chain_id in
   (* N.b. signing a lot of operations may take some time *)
@@ -404,7 +403,6 @@ let inject_preendorsements ~state_recorder state ~preendorsements ~updated_state
           return_some (delegate, operation))
     preendorsements
   >>=? fun signed_operations ->
-  state_recorder ~new_state:updated_state >>=? fun () ->
   (* TODO: add a RPC to inject multiple operations *)
   List.iter_ep
     (fun (delegate, operation) ->
@@ -424,7 +422,6 @@ let inject_preendorsements ~state_recorder state ~preendorsements ~updated_state
           Events.(emit preendorsement_injected (oph, delegate)) >>= fun () ->
           return_unit))
     signed_operations
-  >>=? fun () -> return updated_state
 
 let sign_endorsements state endorsements =
   let cctxt = state.global_state.cctxt in
@@ -491,11 +488,10 @@ let sign_endorsements state endorsements =
           return_some (delegate, operation))
     endorsements
 
-let inject_endorsements ~state_recorder state ~endorsements ~updated_state =
+let inject_endorsements state ~endorsements =
   let cctxt = state.global_state.cctxt in
   let chain_id = state.global_state.chain_id in
   sign_endorsements state endorsements >>=? fun signed_operations ->
-  state_recorder ~new_state:updated_state >>=? fun () ->
   (* TODO: add a RPC to inject multiple operations *)
   List.iter_ep
     (fun (delegate, signed_operation) ->
@@ -510,7 +506,6 @@ let inject_endorsements ~state_recorder state ~endorsements ~updated_state =
       Events.(emit endorsement_injected (oph, delegate)) >>= fun () ->
       return_unit)
     signed_operations
-  >>=? fun () -> return updated_state
 
 let prepare_waiting_for_quorum state =
   let consensus_threshold =
@@ -616,31 +611,34 @@ let synchronize_round state {new_round_proposal; handle_proposal} =
     let new_state = {state with round_state = new_round_state} in
     handle_proposal new_state >>= return
 
+(* TODO: https://gitlab.com/tezos/tezos/-/issues/4539
+   Avoid updating the state here.
+   (See also comment in {!State_transitions.step}.)
+
+   TODO: https://gitlab.com/tezos/tezos/-/issues/4538
+   Improve/clarify when the state is recorded.
+*)
 let rec perform_action ~state_recorder state (action : action) =
   match action with
   | Do_nothing -> state_recorder ~new_state:state >>=? fun () -> return state
   | Inject_block {block_to_bake; updated_state} ->
       inject_block state ~state_recorder block_to_bake ~updated_state
-  | Inject_preendorsements {preendorsements; updated_state} ->
-      inject_preendorsements
-        ~state_recorder
-        state
-        ~preendorsements
-        ~updated_state
-      >>=? fun new_state ->
-      (* We wait for preendorsements to trigger the
-         [Prequorum_reached] event *)
-      start_waiting_for_preendorsement_quorum state >>= fun () ->
-      return new_state
-  | Inject_endorsements {endorsements; updated_state} ->
-      inject_endorsements ~state_recorder state ~endorsements ~updated_state
-      >>=? fun new_state ->
+  | Inject_preendorsements {preendorsements} ->
+      inject_preendorsements state ~preendorsements >>=? fun () ->
+      perform_action ~state_recorder state Watch_proposal
+  | Inject_endorsements {endorsements} ->
+      state_recorder ~new_state:state >>=? fun () ->
+      inject_endorsements state ~endorsements >>=? fun () ->
       (* We wait for endorsements to trigger the [Quorum_reached]
          event *)
-      start_waiting_for_endorsement_quorum state >>= fun () -> return new_state
+      start_waiting_for_endorsement_quorum state >>= fun () -> return state
   | Update_to_level level_update ->
       update_to_level state level_update >>=? fun (new_state, new_action) ->
       perform_action ~state_recorder new_state new_action
   | Synchronize_round round_update ->
       synchronize_round state round_update >>=? fun (new_state, new_action) ->
       perform_action ~state_recorder new_state new_action
+  | Watch_proposal ->
+      (* We wait for preendorsements to trigger the
+           [Prequorum_reached] event *)
+      start_waiting_for_preendorsement_quorum state >>= fun () -> return state
diff --git a/src/proto_016_PtMumbai/lib_delegate/baking_actions.mli b/src/proto_016_PtMumbai/lib_delegate/baking_actions.mli
index da181cda8c3202b695a1e671d5239b9d262c7ee6..91b9bf7729157864c0258c476ae56aeeb30c54ef 100644
--- a/src/proto_016_PtMumbai/lib_delegate/baking_actions.mli
+++ b/src/proto_016_PtMumbai/lib_delegate/baking_actions.mli
@@ -48,14 +48,13 @@ type action =
   | Inject_block of {block_to_bake : block_to_bake; updated_state : state}
   | Inject_preendorsements of {
       preendorsements : (consensus_key_and_delegate * consensus_content) list;
-      updated_state : state;
     }
   | Inject_endorsements of {
       endorsements : (consensus_key_and_delegate * consensus_content) list;
-      updated_state : state;
     }
   | Update_to_level of level_update
   | Synchronize_round of round_update
+  | Watch_proposal
 
 and level_update = {
   new_level_proposal : proposal;
@@ -87,11 +86,9 @@ val inject_block :
   state tzresult Lwt.t
 
 val inject_preendorsements :
-  state_recorder:(new_state:state -> unit tzresult Lwt.t) ->
   state ->
   preendorsements:(consensus_key_and_delegate * consensus_content) list ->
-  updated_state:state ->
-  state tzresult Lwt.t
+  unit tzresult Lwt.t
 
 val sign_endorsements :
   state ->
@@ -99,11 +96,9 @@ val sign_endorsements :
   (consensus_key_and_delegate * packed_operation) list tzresult Lwt.t
 
 val inject_endorsements :
-  state_recorder:(new_state:state -> unit tzresult Lwt.t) ->
   state ->
   endorsements:(consensus_key_and_delegate * consensus_content) list ->
-  updated_state:state ->
-  state tzresult Lwt.t
+  unit tzresult Lwt.t
 
 val prepare_waiting_for_quorum :
   state -> int * (slot:Slot.t -> int) * Operation_worker.candidate
diff --git a/src/proto_016_PtMumbai/lib_delegate/baking_commands.ml b/src/proto_016_PtMumbai/lib_delegate/baking_commands.ml
index 9d76b8745fff52ab03b1a5827649bc4656ee242f..b827d5b7caddb32dd1275d63b705b5f83824f6f3 100644
--- a/src/proto_016_PtMumbai/lib_delegate/baking_commands.ml
+++ b/src/proto_016_PtMumbai/lib_delegate/baking_commands.ml
@@ -166,7 +166,7 @@ let liquidity_baking_toggle_vote_arg =
     liquidity_baking_toggle_vote_parameter
 
 let get_delegates (cctxt : Protocol_client_context.full)
-    (pkhs : Tezos_crypto.Signature.public_key_hash list) =
+    (pkhs : Signature.public_key_hash list) =
   let proj_delegate (alias, public_key_hash, public_key, secret_key_uri) =
     {
       Baking_state.alias = Some alias;
diff --git a/src/proto_016_PtMumbai/lib_delegate/baking_events.ml b/src/proto_016_PtMumbai/lib_delegate/baking_events.ml
index 110ce38543661f136f9202b40e5da2ac07b776e2..9c2af301a0a075638f7ca9a4749da54d4c9e989b 100644
--- a/src/proto_016_PtMumbai/lib_delegate/baking_events.ml
+++ b/src/proto_016_PtMumbai/lib_delegate/baking_events.ml
@@ -498,7 +498,7 @@ module Actions = struct
       ~section
       ~name:"skipping_preendorsement"
       ~level:Error
-      ~msg:"skipping preendorsement for {delegate} -- {trace}"
+      ~msg:"unable to sign preendorsement for {delegate} -- {trace}"
       ~pp1:Baking_state.pp_consensus_key_and_delegate
       ("delegate", Baking_state.consensus_key_and_delegate_encoding)
       ~pp2:Error_monad.pp_print_trace
@@ -509,7 +509,7 @@ module Actions = struct
       ~section
       ~name:"skipping_endorsement"
       ~level:Error
-      ~msg:"skipping endorsement for {delegate} -- {trace}"
+      ~msg:"unable to sign endorsement for {delegate} -- {trace}"
       ~pp1:Baking_state.pp_consensus_key_and_delegate
       ("delegate", Baking_state.consensus_key_and_delegate_encoding)
       ~pp2:Error_monad.pp_print_trace
diff --git a/src/proto_016_PtMumbai/lib_delegate/baking_highwatermarks.ml b/src/proto_016_PtMumbai/lib_delegate/baking_highwatermarks.ml
index 4af172f183fe5e13807314564a2a72cc1c1de5b5..91b56b3e50b1fc062f054f1dcc89668a8c75a03a 100644
--- a/src/proto_016_PtMumbai/lib_delegate/baking_highwatermarks.ml
+++ b/src/proto_016_PtMumbai/lib_delegate/baking_highwatermarks.ml
@@ -100,9 +100,9 @@ let () =
     (fun highwatermark -> Block_previously_endorsed highwatermark)
 
 module DelegateMap = Map.Make (struct
-  type t = Tezos_crypto.Signature.Public_key_hash.t
+  type t = Signature.Public_key_hash.t
 
-  let compare = Tezos_crypto.Signature.Public_key_hash.compare
+  let compare = Signature.Public_key_hash.compare
 end)
 
 let highwatermark_delegate_map_encoding =
@@ -113,7 +113,7 @@ let highwatermark_delegate_map_encoding =
       fun l -> List.fold_left (fun map (k, v) -> add k v map) empty l)
     (list
        (obj2
-          (req "delegate" Tezos_crypto.Signature.Public_key_hash.encoding)
+          (req "delegate" Signature.Public_key_hash.encoding)
           (req "highwatermark" highwatermark_encoding)))
 
 type highwatermarks = {
diff --git a/src/proto_016_PtMumbai/lib_delegate/baking_highwatermarks.mli b/src/proto_016_PtMumbai/lib_delegate/baking_highwatermarks.mli
index 30d4d6f4ea3ea04f27408ebd410cbb49bf72ede8..757b667c58bb68d5628623b9a234c2ab12ae669d 100644
--- a/src/proto_016_PtMumbai/lib_delegate/baking_highwatermarks.mli
+++ b/src/proto_016_PtMumbai/lib_delegate/baking_highwatermarks.mli
@@ -45,7 +45,7 @@ val load :
 val may_sign_block :
   #Protocol_client_context.full ->
   [`Highwatermarks] Baking_files.location ->
-  delegate:Tezos_crypto.Signature.public_key_hash ->
+  delegate:Signature.public_key_hash ->
   level:int32 ->
   round:Round.t ->
   bool tzresult Lwt.t
@@ -53,7 +53,7 @@ val may_sign_block :
 val may_sign_preendorsement :
   #Protocol_client_context.full ->
   [`Highwatermarks] Baking_files.location ->
-  delegate:Tezos_crypto.Signature.public_key_hash ->
+  delegate:Signature.public_key_hash ->
   level:int32 ->
   round:Round.t ->
   bool tzresult Lwt.t
@@ -61,7 +61,7 @@ val may_sign_preendorsement :
 val may_sign_endorsement :
   #Protocol_client_context.full ->
   [`Highwatermarks] Baking_files.location ->
-  delegate:Tezos_crypto.Signature.public_key_hash ->
+  delegate:Signature.public_key_hash ->
   level:int32 ->
   round:Round.t ->
   bool tzresult Lwt.t
@@ -69,7 +69,7 @@ val may_sign_endorsement :
 val record_block :
   #Protocol_client_context.full ->
   [`Highwatermarks] Baking_files.location ->
-  delegate:Tezos_crypto.Signature.public_key_hash ->
+  delegate:Signature.public_key_hash ->
   level:int32 ->
   round:Round.t ->
   unit tzresult Lwt.t
@@ -77,7 +77,7 @@ val record_block :
 val record_preendorsement :
   #Protocol_client_context.full ->
   [`Highwatermarks] Baking_files.location ->
-  delegate:Tezos_crypto.Signature.public_key_hash ->
+  delegate:Signature.public_key_hash ->
   level:int32 ->
   round:Round.t ->
   unit tzresult Lwt.t
@@ -85,7 +85,7 @@ val record_preendorsement :
 val record_endorsement :
   #Protocol_client_context.full ->
   [`Highwatermarks] Baking_files.location ->
-  delegate:Tezos_crypto.Signature.public_key_hash ->
+  delegate:Signature.public_key_hash ->
   level:int32 ->
   round:Round.t ->
   unit tzresult Lwt.t
diff --git a/src/proto_016_PtMumbai/lib_delegate/baking_lib.ml b/src/proto_016_PtMumbai/lib_delegate/baking_lib.ml
index 7ec3ae000cd5f97e8fc8281126379232137dee2a..bb2cb7b3f4ec7e05d4ccbb5b18bbfa0c9aa2fd45 100644
--- a/src/proto_016_PtMumbai/lib_delegate/baking_lib.ml
+++ b/src/proto_016_PtMumbai/lib_delegate/baking_lib.ml
@@ -86,17 +86,7 @@ let preendorse (cctxt : Protocol_client_context.full) ?(force = false) delegates
           Baking_state.pp_consensus_key_and_delegate)
       (List.map fst consensus_list)
   in
-  let state_recorder ~new_state =
-    Baking_state.may_record_new_state ~previous_state:state ~new_state
-  in
-  let* _ =
-    Baking_actions.inject_preendorsements
-      ~state_recorder
-      state
-      ~preendorsements:consensus_list
-      ~updated_state:state
-  in
-  return_unit
+  Baking_actions.inject_preendorsements state ~preendorsements:consensus_list
 
 let endorse (cctxt : Protocol_client_context.full) ?(force = false) delegates =
   let open State_transitions in
@@ -126,17 +116,10 @@ let endorse (cctxt : Protocol_client_context.full) ?(force = false) delegates =
           Baking_state.pp_consensus_key_and_delegate)
       (List.map fst consensus_list)
   in
-  let state_recorder ~new_state =
-    Baking_state.may_record_new_state ~previous_state:state ~new_state
-  in
-  let* _ =
-    Baking_actions.inject_endorsements
-      ~state_recorder
-      state
-      ~endorsements:consensus_list
-      ~updated_state:state
+  let* () =
+    Baking_state.may_record_new_state ~previous_state:state ~new_state:state
   in
-  return_unit
+  Baking_actions.inject_endorsements state ~endorsements:consensus_list
 
 let bake_at_next_level state =
   let open Lwt_result_syntax in
diff --git a/src/proto_016_PtMumbai/lib_delegate/baking_nonces.ml b/src/proto_016_PtMumbai/lib_delegate/baking_nonces.ml
index 5af73f61735e63a47f20d9c57afe2e750ac24ed9..fc1c9ada635ac59fc205b047b43e9a5b0f06aee3 100644
--- a/src/proto_016_PtMumbai/lib_delegate/baking_nonces.ml
+++ b/src/proto_016_PtMumbai/lib_delegate/baking_nonces.ml
@@ -239,9 +239,7 @@ let inject_seed_nonce_revelation (cctxt : #Protocol_client_context.full) ~chain
             ~nonce
             ()
           >>=? fun bytes ->
-          let bytes =
-            Tezos_crypto.Signature.concat bytes Tezos_crypto.Signature.zero
-          in
+          let bytes = Signature.concat bytes Signature.zero in
           Shell_services.Injection.operation ~async:true cctxt ~chain bytes
           >>=? fun oph ->
           Events.(
diff --git a/src/proto_016_PtMumbai/lib_delegate/baking_scheduling.ml b/src/proto_016_PtMumbai/lib_delegate/baking_scheduling.ml
index 38d42a06cc3df5e395c0c4bea0b847273fc490a0..96350fe3ba3e2600154a7750b933f2b8fe12f492 100644
--- a/src/proto_016_PtMumbai/lib_delegate/baking_scheduling.ml
+++ b/src/proto_016_PtMumbai/lib_delegate/baking_scheduling.ml
@@ -68,9 +68,9 @@ let find_in_known_round_intervals known_round_intervals ~predecessor_timestamp
       {predecessor_timestamp; predecessor_round; time_interval = (now, now)})
 
 (** Memoization wrapper for [Round.timestamp_of_round]. *)
-let timestamp_of_round known_timestamps round_durations ~predecessor_timestamp
-    ~predecessor_round ~round =
+let timestamp_of_round state ~predecessor_timestamp ~predecessor_round ~round =
   let open Baking_cache in
+  let known_timestamps = state.global_state.cache.known_timestamps in
   match
     Timestamp_of_round_cache.find_opt
       known_timestamps
@@ -79,7 +79,7 @@ let timestamp_of_round known_timestamps round_durations ~predecessor_timestamp
   (* Compute and register the timestamp if not already existing. *)
   | None ->
       Protocol.Alpha_context.Round.timestamp_of_round
-        round_durations
+        state.global_state.round_durations
         ~predecessor_timestamp
         ~predecessor_round
         ~round
@@ -220,32 +220,18 @@ let compute_next_round_time state =
            repropose a block at next level. *)
         None
     | None -> (
-        let first_round_duration =
-          state.global_state.constants.parametric.minimal_block_delay
-        in
-        let delay_increment_per_round =
-          state.global_state.constants.parametric.delay_increment_per_round
-        in
+        let predecessor_timestamp = proposal.predecessor.shell.timestamp in
+        let predecessor_round = proposal.predecessor.round in
+        let next_round = Round.succ state.round_state.current_round in
         match
-          Round.Durations.create_opt
-            ~first_round_duration
-            ~delay_increment_per_round
+          timestamp_of_round
+            state
+            ~predecessor_timestamp
+            ~predecessor_round
+            ~round:next_round
         with
-        | Some round_durations -> (
-            let predecessor_timestamp = proposal.predecessor.shell.timestamp in
-            let predecessor_round = proposal.predecessor.round in
-            let next_round = Round.succ state.round_state.current_round in
-            match
-              timestamp_of_round
-                state.global_state.cache.known_timestamps
-                round_durations
-                ~predecessor_timestamp
-                ~predecessor_round
-                ~round:next_round
-            with
-            | Ok timestamp -> Some (timestamp, next_round)
-            | _ -> assert false)
-        | None -> assert false)
+        | Ok timestamp -> Some (timestamp, next_round)
+        | _ -> assert false)
 
 (** [first_potential_round_at_next_level state ~earliest_round] yields
     an optional pair of the earliest possible round (at or after
@@ -387,8 +373,7 @@ let compute_next_potential_baking_time_at_next_level state =
                           >>= fun () -> Lwt.return_none
                       | None | Some _ -> (
                           timestamp_of_round
-                            state.global_state.cache.known_timestamps
-                            round_durations
+                            state
                             ~predecessor_timestamp
                             ~predecessor_round
                             ~round:first_potential_round
@@ -475,13 +460,14 @@ let compute_next_timeout state : Baking_state.timeout_kind Lwt.t tzresult Lwt.t
   let wait_baking_time_next_level (next_baking_time, next_baking_round) =
     let now = Time.System.now () in
     let delay = Ptime.diff (Time.System.of_protocol_exn next_baking_time) now in
-    Events.(emit waiting_time_to_bake (delay, next_baking_time)) >>= fun () ->
     match sleep_until next_baking_time with
     | None ->
         Events.(emit no_need_to_wait_for_proposal ()) >>= fun () ->
         return
           (Lwt.return (Time_to_bake_next_level {at_round = next_baking_round}))
     | Some t ->
+        Events.(emit waiting_time_to_bake (delay, next_baking_time))
+        >>= fun () ->
         return
           ( t >>= fun () ->
             Lwt.return (Time_to_bake_next_level {at_round = next_baking_round})
@@ -652,13 +638,7 @@ let create_initial_state cctxt ?(synchronize = true) ~chain config
     }
   in
   (if synchronize then
-   let round_durations =
-     Stdlib.Option.get
-     @@ Round.Durations.create_opt
-          ~first_round_duration:constants.parametric.minimal_block_delay
-          ~delay_increment_per_round:
-            constants.parametric.delay_increment_per_round
-   in
+   create_round_durations constants >>? fun round_durations ->
    Baking_actions.compute_round current_proposal round_durations
    >>? fun current_round -> ok {current_round; current_phase = Idle}
   else ok {Baking_state.current_round = Round.zero; current_phase = Idle})
diff --git a/src/proto_016_PtMumbai/lib_delegate/baking_state.ml b/src/proto_016_PtMumbai/lib_delegate/baking_state.ml
index 984c2bbbd2378d30dc3db42766bad0f93706ce4f..475306cac7d8a5782338e0a041cda4354771fe6a 100644
--- a/src/proto_016_PtMumbai/lib_delegate/baking_state.ml
+++ b/src/proto_016_PtMumbai/lib_delegate/baking_state.ml
@@ -31,8 +31,8 @@ open Protocol_client_context
     public key, its public key hash, and its secret key. *)
 type consensus_key = {
   alias : string option;
-  public_key : Tezos_crypto.Signature.Public_key.t;
-  public_key_hash : Tezos_crypto.Signature.Public_key_hash.t;
+  public_key : Signature.Public_key.t;
+  public_key_hash : Signature.Public_key_hash.t;
   secret_key_uri : Client_keys.sk_uri;
 }
 
@@ -56,48 +56,39 @@ let consensus_key_encoding =
       })
     (obj4
        (req "alias" (option string))
-       (req "public_key" Tezos_crypto.Signature.Public_key.encoding)
-       (req "public_key_hash" Tezos_crypto.Signature.Public_key_hash.encoding)
+       (req "public_key" Signature.Public_key.encoding)
+       (req "public_key_hash" Signature.Public_key_hash.encoding)
        (req "secret_key_uri" string))
 
 let pp_consensus_key fmt {alias; public_key_hash; _} =
   match alias with
-  | None ->
-      Format.fprintf
-        fmt
-        "%a"
-        Tezos_crypto.Signature.Public_key_hash.pp
-        public_key_hash
+  | None -> Format.fprintf fmt "%a" Signature.Public_key_hash.pp public_key_hash
   | Some alias ->
       Format.fprintf
         fmt
         "%s (%a)"
         alias
-        Tezos_crypto.Signature.Public_key_hash.pp
+        Signature.Public_key_hash.pp
         public_key_hash
 
-type consensus_key_and_delegate =
-  consensus_key * Tezos_crypto.Signature.Public_key_hash.t
+type consensus_key_and_delegate = consensus_key * Signature.Public_key_hash.t
 
 let consensus_key_and_delegate_encoding =
   let open Data_encoding in
   merge_objs
     consensus_key_encoding
-    (obj1 (req "delegate" Tezos_crypto.Signature.Public_key_hash.encoding))
+    (obj1 (req "delegate" Signature.Public_key_hash.encoding))
 
 let pp_consensus_key_and_delegate fmt (consensus_key, delegate) =
-  if
-    Tezos_crypto.Signature.Public_key_hash.equal
-      consensus_key.public_key_hash
-      delegate
-  then pp_consensus_key fmt consensus_key
+  if Signature.Public_key_hash.equal consensus_key.public_key_hash delegate then
+    pp_consensus_key fmt consensus_key
   else
     Format.fprintf
       fmt
       "%a@,on behalf of %a"
       pp_consensus_key
       consensus_key
-      Tezos_crypto.Signature.Public_key_hash.pp
+      Signature.Public_key_hash.pp
       delegate
 
 type validation_mode = Node | Local of Abstract_context_index.t
@@ -250,7 +241,7 @@ module SlotMap : Map.S with type key = Slot.t = Map.Make (Slot)
     list of slots (i.e., a list of position indexes in the slot map, in
     other words the list of rounds when it will be the proposer), and
     its endorsing power. *)
-type endorsing_slot = {slots : Slot.t list; endorsing_power : int}
+type endorsing_slot = {first_slot : Slot.t; endorsing_power : int}
 
 (* FIXME: determine if the slot map should contain all slots or just
    the first one *)
@@ -358,6 +349,9 @@ type state = {
 
 type t = state
 
+let update_current_phase state new_phase =
+  {state with round_state = {state.round_state with current_phase = new_phase}}
+
 type timeout_kind =
   | End_of_round of {ending_round : Round.t}
   | Time_to_bake_next_level of {at_round : Round.t}
@@ -760,7 +754,7 @@ module DelegateSet = struct
     type t = consensus_key
 
     let compare {public_key_hash = pkh; _} {public_key_hash = pkh'; _} =
-      Tezos_crypto.Signature.Public_key_hash.compare pkh pkh'
+      Signature.Public_key_hash.compare pkh pkh'
   end)
 
   let find_pkh pkh s =
@@ -768,8 +762,8 @@ module DelegateSet = struct
     try
       iter
         (fun ({public_key_hash; _} as delegate) ->
-          if Tezos_crypto.Signature.Public_key_hash.equal pkh public_key_hash
-          then raise (Found delegate)
+          if Signature.Public_key_hash.equal pkh public_key_hash then
+            raise (Found delegate)
           else ())
         s ;
       None
@@ -788,7 +782,12 @@ let compute_delegate_slots (cctxt : Protocol_client_context.full)
     List.fold_left
       (fun (own_map, all_map) slot ->
         let {Plugin.RPC.Validators.consensus_key; delegate; slots; _} = slot in
-        let endorsing_slot = {endorsing_power = List.length slots; slots} in
+        let endorsing_slot =
+          {
+            endorsing_power = List.length slots;
+            first_slot = Stdlib.List.hd slots;
+          }
+        in
         let all_map =
           List.fold_left
             (fun all_map slot -> SlotMap.add slot endorsing_slot all_map)
@@ -922,13 +921,13 @@ let pp_elected_block fmt {proposal; endorsement_qc} =
     proposal.block
     (List.length endorsement_qc)
 
-let pp_endorsing_slot fmt (consensus_key_and_delegate, {slots; endorsing_power})
-    =
+let pp_endorsing_slot fmt
+    (consensus_key_and_delegate, {first_slot; endorsing_power}) =
   Format.fprintf
     fmt
-    "slots: @[<h>[%a]@],@ delegate: %a,@ endorsing_power: %d"
-    Format.(pp_print_list ~pp_sep:pp_print_space Slot.pp)
-    slots
+    "slots: @[<h>first_slot: %a@],@ delegate: %a,@ endorsing_power: %d"
+    Slot.pp
+    first_slot
     pp_consensus_key_and_delegate
     consensus_key_and_delegate
     endorsing_power
diff --git a/src/proto_016_PtMumbai/lib_delegate/baking_state.mli b/src/proto_016_PtMumbai/lib_delegate/baking_state.mli
index 34ce3743c4ade8c291590038ccbfaa90cfcde50e..fef6d3ccc33610ab55b5439c5e6b606114b422cf 100644
--- a/src/proto_016_PtMumbai/lib_delegate/baking_state.mli
+++ b/src/proto_016_PtMumbai/lib_delegate/baking_state.mli
@@ -28,8 +28,8 @@ open Alpha_context
 
 type consensus_key = {
   alias : string option;
-  public_key : Tezos_crypto.Signature.public_key;
-  public_key_hash : Tezos_crypto.Signature.public_key_hash;
+  public_key : Signature.public_key;
+  public_key_hash : Signature.public_key_hash;
   secret_key_uri : Client_keys.sk_uri;
 }
 
@@ -37,8 +37,7 @@ val consensus_key_encoding : consensus_key Data_encoding.t
 
 val pp_consensus_key : Format.formatter -> consensus_key -> unit
 
-type consensus_key_and_delegate =
-  consensus_key * Tezos_crypto.Signature.Public_key_hash.t
+type consensus_key_and_delegate = consensus_key * Signature.Public_key_hash.t
 
 val consensus_key_and_delegate_encoding :
   consensus_key_and_delegate Data_encoding.t
@@ -97,7 +96,7 @@ val round_of_shell_header : Block_header.shell_header -> Round.t tzresult
 
 module SlotMap : Map.S with type key = Slot.t
 
-type endorsing_slot = {slots : Slot.t list; endorsing_power : int}
+type endorsing_slot = {first_slot : Slot.t; endorsing_power : int}
 
 type delegate_slots = {
   own_delegate_slots : (consensus_key_and_delegate * endorsing_slot) SlotMap.t;
@@ -147,6 +146,8 @@ type state = {
 
 type t = state
 
+val update_current_phase : t -> phase -> t
+
 type timeout_kind =
   | End_of_round of {ending_round : Round.t}
   | Time_to_bake_next_level of {at_round : Round.t}
diff --git a/src/proto_016_PtMumbai/lib_delegate/baking_vdf.ml b/src/proto_016_PtMumbai/lib_delegate/baking_vdf.ml
index cdceb772344abca5048c1fed5458bdb288e711c4..c0e97b55ea74b76b00a2368a7f96d14ab4dc9880 100644
--- a/src/proto_016_PtMumbai/lib_delegate/baking_vdf.ml
+++ b/src/proto_016_PtMumbai/lib_delegate/baking_vdf.ml
@@ -156,7 +156,7 @@ let inject_vdf_revelation cctxt hash chain_id solution =
       ~solution
       ()
   in
-  let bytes = Tezos_crypto.Signature.concat bytes Tezos_crypto.Signature.zero in
+  let bytes = Signature.concat bytes Signature.zero in
   Shell_services.Injection.operation cctxt ~chain bytes
 
 (* Checks if the VDF setup saved in the state is equal to the one computed
diff --git a/src/proto_016_PtMumbai/lib_delegate/block_forge.ml b/src/proto_016_PtMumbai/lib_delegate/block_forge.ml
index 917133e0e5534b6efb4ea169c29e83d87ca2fcca..062306d6367d7a0c503a6dfa2f283a45716dc282 100644
--- a/src/proto_016_PtMumbai/lib_delegate/block_forge.ml
+++ b/src/proto_016_PtMumbai/lib_delegate/block_forge.ml
@@ -52,7 +52,7 @@ let forge_faked_protocol_data ?(payload_hash = Block_payload_hash.zero)
           proof_of_work_nonce = Baking_pow.empty_proof_of_work_nonce;
           liquidity_baking_toggle_vote;
         };
-      signature = Tezos_crypto.Signature.zero;
+      signature = Signature.zero;
     }
 
 let convert_operation (op : packed_operation) : Tezos_base.Operation.t =
@@ -389,7 +389,7 @@ let forge (cctxt : #Protocol_client_context.full) ~chain_id ~pred_info
   let unsigned_block_header =
     {
       Block_header.shell = shell_header;
-      protocol_data = {contents; signature = Tezos_crypto.Signature.zero};
+      protocol_data = {contents; signature = Signature.zero};
     }
   in
   return {unsigned_block_header; operations}
diff --git a/src/proto_016_PtMumbai/lib_delegate/client_baking_denunciation.ml b/src/proto_016_PtMumbai/lib_delegate/client_baking_denunciation.ml
index cb6f6a02e66edb3399c16c5d855153516148a66d..2ebc4af5961ebbaaaca22a8a95d8ebd310d291f0 100644
--- a/src/proto_016_PtMumbai/lib_delegate/client_baking_denunciation.ml
+++ b/src/proto_016_PtMumbai/lib_delegate/client_baking_denunciation.ml
@@ -40,7 +40,7 @@ module HLevel = Hashtbl.Make (struct
 end)
 
 (* Blocks are associated to the delegates who baked them *)
-module Delegate_Map = Map.Make (Tezos_crypto.Signature.Public_key_hash)
+module Delegate_Map = Map.Make (Signature.Public_key_hash)
 
 (* (pre)endorsements are associated to the slot they are injected
    with; we rely on the fact that there is a unique canonical slot
@@ -175,9 +175,7 @@ let process_consensus_op (type kind) cctxt
         ~op2
         ()
       >>=? fun bytes ->
-      let bytes =
-        Tezos_crypto.Signature.concat bytes Tezos_crypto.Signature.zero
-      in
+      let bytes = Signature.concat bytes Signature.zero in
       let double_op_detected, double_op_denounced =
         Events.(
           match op_kind with
@@ -303,9 +301,7 @@ let process_block (cctxt : #Protocol_client_context.full) state
             ~bh2
             ()
           >>=? fun bytes ->
-          let bytes =
-            Tezos_crypto.Signature.concat bytes Tezos_crypto.Signature.zero
-          in
+          let bytes = Signature.concat bytes Signature.zero in
           Events.(emit double_baking_detected) () >>= fun () ->
           Shell_services.Injection.operation cctxt ~chain bytes
           >>=? fun op_hash ->
diff --git a/src/proto_016_PtMumbai/lib_delegate/operation_selection.ml b/src/proto_016_PtMumbai/lib_delegate/operation_selection.ml
index 089f4b439a9309eb74babbc42dd5f7ea9282ebb4..9a4fbf4d0b92ed64ffd2016bea743c8cebfca75b 100644
--- a/src/proto_016_PtMumbai/lib_delegate/operation_selection.ml
+++ b/src/proto_016_PtMumbai/lib_delegate/operation_selection.ml
@@ -57,9 +57,7 @@ module PrioritizedManagerSet = Set.Make (struct
   let compare {source; counter; weight; op; _}
       {source = source'; counter = counter'; weight = weight'; op = op'; _} =
     (* Be careful with the [compare] *)
-    let cmp_src =
-      Tezos_crypto.Signature.Public_key_hash.compare source source'
-    in
+    let cmp_src = Signature.Public_key_hash.compare source source' in
     if cmp_src = 0 then
       (* we want the smallest counter first *)
       let c = Manager_counter.compare counter counter' in
diff --git a/src/proto_016_PtMumbai/lib_delegate/state_transitions.ml b/src/proto_016_PtMumbai/lib_delegate/state_transitions.ml
index 6e8dd27e628468da9c64a5493c1d137d5a965e28..d39c05dbc8cdd858a589a671db6b74db8b78ebb7 100644
--- a/src/proto_016_PtMumbai/lib_delegate/state_transitions.ml
+++ b/src/proto_016_PtMumbai/lib_delegate/state_transitions.ml
@@ -81,7 +81,7 @@ let make_consensus_list state proposal =
   SlotMap.fold
     (fun _slot (consensus_key_and_delegate, slots) acc ->
       ( consensus_key_and_delegate,
-        {slot = Stdlib.List.hd slots.slots; level; round; block_payload_hash} )
+        {slot = slots.first_slot; level; round; block_payload_hash} )
       :: acc)
     state.level_state.delegate_slots.own_delegate_slots
     []
@@ -90,16 +90,10 @@ let make_consensus_list state proposal =
 (* If we do not have any slots, we won't inject any operation but we
    will still participate to determine an elected block *)
 let make_preendorse_action state proposal =
-  let updated_state =
-    let round_state =
-      {state.round_state with current_phase = Awaiting_preendorsements}
-    in
-    {state with round_state}
-  in
   let preendorsements : (consensus_key_and_delegate * consensus_content) list =
     make_consensus_list state proposal
   in
-  Inject_preendorsements {preendorsements; updated_state}
+  Inject_preendorsements {preendorsements}
 
 let update_proposal state proposal =
   Events.(emit updating_latest_proposal proposal.block.hash) >>= fun () ->
@@ -120,12 +114,13 @@ let preendorse state proposal =
   if Protocol_hash.(proposal.block.protocol <> proposal.block.next_protocol)
   then
     (* We do not preendorse the first transition block *)
-    let new_round_state = {state.round_state with current_phase = Idle} in
-    let new_state = {state with round_state = new_round_state} in
+    let new_state = update_current_phase state Idle in
     Lwt.return (new_state, Do_nothing)
   else
     Events.(emit attempting_preendorse_proposal proposal.block.hash)
-    >>= fun () -> Lwt.return (state, make_preendorse_action state proposal)
+    >>= fun () ->
+    let new_state = update_current_phase state Awaiting_preendorsements in
+    Lwt.return (new_state, make_preendorse_action state proposal)
 
 let extract_pqc state (new_proposal : proposal) =
   match new_proposal.block.prequorum with
@@ -247,7 +242,13 @@ let rec handle_new_proposal state (new_proposal : proposal) =
                 | Some {round; _} when Round.(locked_round.round < round) ->
                     (* This PQC is above our locked_round, we can preendorse it *)
                     preendorse new_state new_proposal
-                | _ -> Lwt.return (new_state, Do_nothing))
+                | _ ->
+                    (* We shouldn't preendorse this proposal, but we should at
+                       least watch (pre)quorums events on it *)
+                    let new_state =
+                      update_current_phase new_state Awaiting_preendorsements
+                    in
+                    Lwt.return (new_state, Watch_proposal))
           | None ->
               (* Otherwise, we did not lock on any payload, thus we can
                  preendorse it *)
@@ -413,10 +414,7 @@ let propose_fresh_block_action ~endorsements ?last_proposal
   let kind = Fresh operation_pool in
   Events.(emit proposing_fresh_block (delegate, round)) >>= fun () ->
   let block_to_bake = {predecessor; round; delegate; kind} in
-  let updated_state =
-    let new_round_state = {state.round_state with current_phase = Idle} in
-    {state with round_state = new_round_state}
-  in
+  let updated_state = update_current_phase state Idle in
   Lwt.return @@ Inject_block {block_to_bake; updated_state}
 
 let propose_block_action state delegate round (proposal : proposal) =
@@ -503,10 +501,7 @@ let propose_block_action state delegate round (proposal : proposal) =
       let block_to_bake =
         {predecessor = proposal.predecessor; round; delegate; kind}
       in
-      let updated_state =
-        let new_round_state = {state.round_state with current_phase = Idle} in
-        {state with round_state = new_round_state}
-      in
+      let updated_state = update_current_phase state Idle in
       Lwt.return @@ Inject_block {block_to_bake; updated_state}
 
 let end_of_round state current_round =
@@ -529,8 +524,7 @@ let end_of_round state current_round =
       (* We don't have any delegate that may propose a new block for
          this round -- We will wait for preendorsements when the next
          level block arrive. Meanwhile, we are idle *)
-      let new_round_state = {new_state.round_state with current_phase = Idle} in
-      let new_state = {state with round_state = new_round_state} in
+      let new_state = update_current_phase new_state Idle in
       do_nothing new_state
   | Some (delegate, _) ->
       let last_proposal = state.level_state.latest_proposal.block in
@@ -588,20 +582,10 @@ let update_locked_round state round payload_hash =
   {state with level_state = new_level_state}
 
 let make_endorse_action state proposal =
-  let updated_state =
-    let new_round_state =
-      {state.round_state with current_phase = Awaiting_endorsements}
-    in
-    let new_state = {state with round_state = new_round_state} in
-    update_locked_round
-      new_state
-      proposal.block.round
-      proposal.block.payload_hash
-  in
   let endorsements : (consensus_key_and_delegate * consensus_content) list =
     make_consensus_list state proposal
   in
-  Inject_endorsements {endorsements; updated_state}
+  Inject_endorsements {endorsements}
 
 let prequorum_reached_when_awaiting_preendorsements state candidate
     preendorsements =
@@ -642,6 +626,13 @@ let prequorum_reached_when_awaiting_preendorsements state candidate
           else state.level_state
     in
     let new_state = {state with level_state = new_level_state} in
+    let new_state =
+      update_locked_round
+        new_state
+        latest_proposal.block.round
+        latest_proposal.block.payload_hash
+    in
+    let new_state = update_current_phase new_state Awaiting_endorsements in
     Lwt.return (new_state, make_endorse_action new_state latest_proposal)
 
 let quorum_reached_when_waiting_endorsements state candidate endorsement_qc =
@@ -674,6 +665,9 @@ let quorum_reached_when_waiting_endorsements state candidate endorsement_qc =
 
 (* Hypothesis:
    - The state is not to be modified outside this module
+     (NB: there are exceptions in Baking_actions: the corner cases
+     [update_to_level] and [synchronize_round] and
+     the hack used by [inject_block])
 
    - new_proposal's received blocks are expected to belong to our current
      round
diff --git a/src/proto_016_PtMumbai/lib_delegate/state_transitions.mli b/src/proto_016_PtMumbai/lib_delegate/state_transitions.mli
index 9dde0efaf02bba9e9c9ca327a709020e226757e3..adc5843123296c8ee79ce2c744a404011edaf46a 100644
--- a/src/proto_016_PtMumbai/lib_delegate/state_transitions.mli
+++ b/src/proto_016_PtMumbai/lib_delegate/state_transitions.mli
@@ -23,6 +23,9 @@
 (*                                                                           *)
 (*****************************************************************************)
 
+(** This module, and in particular the {!step} function, modifies the automaton
+    state, while {!Baking_actions} performs potentially failing side-effects. *)
+
 open Protocol
 open Alpha_context
 open Baking_state
diff --git a/src/proto_016_PtMumbai/lib_delegate/test/mockup_simulator/mockup_simulator.ml b/src/proto_016_PtMumbai/lib_delegate/test/mockup_simulator/mockup_simulator.ml
index 4cadea890daaf394e6626e5b8b88280c6d4a1151..346cea3ee712a470aa51077536cdf5a9cc642167 100644
--- a/src/proto_016_PtMumbai/lib_delegate/test/mockup_simulator/mockup_simulator.ml
+++ b/src/proto_016_PtMumbai/lib_delegate/test/mockup_simulator/mockup_simulator.ml
@@ -842,7 +842,7 @@ let baker_process ~(delegates : Baking_state.consensus_key list) ~base_dir
   Lwt.pick [listener_process (); baker_process ()] >>=? fun () ->
   User_hooks.check_chain_on_success ~chain:state.chain
 
-let genesis_protocol_data (baker_sk : Tezos_crypto.Signature.secret_key)
+let genesis_protocol_data (baker_sk : Signature.secret_key)
     (predecessor_hash : Block_hash.t) (block_header : Block_header.shell_header)
     : Bytes.t =
   let proof_of_work_nonce =
@@ -871,7 +871,7 @@ let genesis_protocol_data (baker_sk : Tezos_crypto.Signature.secret_key)
       (block_header, contents)
   in
   let signature =
-    Tezos_crypto.Signature.sign
+    Signature.sign
       ~watermark:
         Alpha_context.Block_header.(to_watermark (Block_header chain_id))
       baker_sk
@@ -887,7 +887,7 @@ let deduce_baker_sk
       (Protocol.Alpha_context.Parameters.bootstrap_account
       * Tezos_mockup_commands.Mockup_wallet.bootstrap_secret)
       list) (total_accounts : int) (level : int) :
-    Tezos_crypto.Signature.secret_key tzresult Lwt.t =
+    Signature.secret_key tzresult Lwt.t =
   (match (total_accounts, level) with
   | _, 0 -> return 0 (* apparently this doesn't really matter *)
   | _ ->
@@ -902,8 +902,7 @@ let deduce_baker_sk
     |> WithExceptions.Option.get ~loc:__LOC__
   in
   let secret_key =
-    Tezos_crypto.Signature.Secret_key.of_b58check_exn
-      (Uri.path (secret.sk_uri :> Uri.t))
+    Signature.Secret_key.of_b58check_exn (Uri.path (secret.sk_uri :> Uri.t))
   in
   return secret_key
 
@@ -1078,8 +1077,7 @@ type config = {
   round0 : int64;
   round1 : int64;
   timeout : int;
-  delegate_selection :
-    (int32 * (int32 * Tezos_crypto.Signature.public_key_hash) list) list;
+  delegate_selection : (int32 * (int32 * Signature.public_key_hash) list) list;
   initial_seed : State_hash.t option;
   consensus_committee_size : int;
   consensus_threshold : int;
@@ -1215,7 +1213,7 @@ let check_block_signature ~block_hash ~(block_header : Block_header.t)
       (block_header.shell, protocol_data.contents)
   in
   if
-    Tezos_crypto.Signature.check
+    Signature.check
       ~watermark:
         Alpha_context.Block_header.(to_watermark (Block_header chain_id))
       public_key
@@ -1227,7 +1225,7 @@ let check_block_signature ~block_hash ~(block_header : Block_header.t)
       "unexpected signature for %a; tried with %a@."
       Block_hash.pp
       block_hash
-      Tezos_crypto.Signature.Public_key.pp
+      Signature.Public_key.pp
       public_key
 
 type op_predicate =
@@ -1262,7 +1260,7 @@ let op_is_signed_by ~public_key (op_hash : Operation_hash.t)
                 Alpha_context.Operation.to_watermark (Endorsement chain_id)
             | Preendorsement _ ->
                 Alpha_context.Operation.to_watermark (Preendorsement chain_id)
-            | _ -> Tezos_crypto.Signature.Generic_operation)
+            | _ -> Signature.Generic_operation)
       | _ -> failwith "unexpected contents in %a@." Operation_hash.pp op_hash)
       >>=? fun watermark ->
       match d.signature with
@@ -1278,7 +1276,7 @@ let op_is_signed_by ~public_key (op_hash : Operation_hash.t)
               (op.shell, Contents_list d.contents)
           in
           return
-            (Tezos_crypto.Signature.check
+            (Signature.check
                ~watermark
                public_key
                signature
diff --git a/src/proto_016_PtMumbai/lib_delegate/test/mockup_simulator/mockup_simulator.mli b/src/proto_016_PtMumbai/lib_delegate/test/mockup_simulator/mockup_simulator.mli
index 2fc5f544597ab405192ac9fbdbbe698fd555af76..c01782653bdff6cf45ea010cf9df23ed1bd58741 100644
--- a/src/proto_016_PtMumbai/lib_delegate/test/mockup_simulator/mockup_simulator.mli
+++ b/src/proto_016_PtMumbai/lib_delegate/test/mockup_simulator/mockup_simulator.mli
@@ -139,8 +139,7 @@ type config = {
       (** Maximal duration of the test. If the test takes
                      longer to terminate it'll be aborted with an
                      error. *)
-  delegate_selection :
-    (int32 * (int32 * Tezos_crypto.Signature.public_key_hash) list) list;
+  delegate_selection : (int32 * (int32 * Signature.public_key_hash) list) list;
       (** Desired selection of delegates per level/round *)
   initial_seed : State_hash.t option;
       (** Optional initial seed for protocol (used to control delegate selection) *)
@@ -172,21 +171,21 @@ val default_config : config
    to the final result. *)
 val run : ?config:config -> (int * (module Hooks)) list -> unit tzresult Lwt.t
 
-val bootstrap1 : Tezos_crypto.Signature.public_key
+val bootstrap1 : Signature.public_key
 
-val bootstrap2 : Tezos_crypto.Signature.public_key
+val bootstrap2 : Signature.public_key
 
-val bootstrap3 : Tezos_crypto.Signature.public_key
+val bootstrap3 : Signature.public_key
 
-val bootstrap4 : Tezos_crypto.Signature.public_key
+val bootstrap4 : Signature.public_key
 
-val bootstrap5 : Tezos_crypto.Signature.public_key
+val bootstrap5 : Signature.public_key
 
 (** Check if a block header is signed by a given delegate. *)
 val check_block_signature :
   block_hash:Block_hash.t ->
   block_header:Block_header.t ->
-  public_key:Tezos_crypto.Signature.public_key ->
+  public_key:Signature.public_key ->
   unit tzresult Lwt.t
 
 (** A shortcut type for predicates on operations. *)
@@ -216,8 +215,7 @@ val mempool_has_op_ref :
   unit tzresult Lwt.t
 
 (** Check if an operation is signed by the given delegate. *)
-val op_is_signed_by :
-  public_key:Tezos_crypto.Signature.public_key -> op_predicate
+val op_is_signed_by : public_key:Signature.public_key -> op_predicate
 
 (** Check that an operation is a preendorsement. *)
 val op_is_preendorsement : ?level:int32 -> ?round:int32 -> op_predicate
diff --git a/src/proto_016_PtMumbai/lib_delegate/test/tenderbrute/lib/tenderbrute.ml b/src/proto_016_PtMumbai/lib_delegate/test/tenderbrute/lib/tenderbrute.ml
index fdc0a6dc5abb8041ee537196f2761b845287073b..ce3f8bba638032e0e0d5ca935d40cf774956ea05 100644
--- a/src/proto_016_PtMumbai/lib_delegate/test/tenderbrute/lib/tenderbrute.ml
+++ b/src/proto_016_PtMumbai/lib_delegate/test/tenderbrute/lib/tenderbrute.ml
@@ -26,9 +26,7 @@
 open Protocol
 
 type delegate_selection =
-  (Raw_level_repr.t
-  * (Round_repr.t * Tezos_crypto.Signature.public_key_hash) list)
-  list
+  (Raw_level_repr.t * (Round_repr.t * Signature.public_key_hash) list) list
 
 module LevelRoundMap = Map.Make (struct
   type t = Level_repr.t * Round_repr.t
@@ -105,12 +103,8 @@ let check ctxt ~selection =
           Delegate_sampler.baking_rights_owner ctxt level ~round
           >|= Environment.wrap_tzresult
           >>=? fun (ctxt, _, pk) ->
-          if
-            not
-              (Tezos_crypto.Signature.Public_key_hash.equal
-                 delegate
-                 pk.delegate)
-          then raise Exit
+          if not (Signature.Public_key_hash.equal delegate pk.delegate) then
+            raise Exit
           else return ctxt)
         selection
         ctxt
diff --git a/src/proto_016_PtMumbai/lib_delegate/test/tenderbrute/lib/tenderbrute.mli b/src/proto_016_PtMumbai/lib_delegate/test/tenderbrute/lib/tenderbrute.mli
index c13cc23edb6002253f31f4d91e524a6833584dfd..7b6915d2cfd283a3fed1b2dd55a2e2be4b3194fb 100644
--- a/src/proto_016_PtMumbai/lib_delegate/test/tenderbrute/lib/tenderbrute.mli
+++ b/src/proto_016_PtMumbai/lib_delegate/test/tenderbrute/lib/tenderbrute.mli
@@ -29,9 +29,7 @@ open Protocol
     one can provide a public key hash that would be the proposer. All non-
     specified level and rounds are not constrained. *)
 type delegate_selection =
-  (Raw_level_repr.t
-  * (Round_repr.t * Tezos_crypto.Signature.public_key_hash) list)
-  list
+  (Raw_level_repr.t * (Round_repr.t * Signature.public_key_hash) list) list
 
 (** Brute-force an initial seed nonce for the desired delegate selection.
     When found, the seed nonce is returned as a byte sequence of size 32. If
diff --git a/src/proto_016_PtMumbai/lib_delegate/test/tenderbrute/tenderbrute_main.ml b/src/proto_016_PtMumbai/lib_delegate/test/tenderbrute/tenderbrute_main.ml
index 123db4e59248226fa738d75b7e6225a6cac5e88d..f3558b1a198548993524bde2373b0a8f531d48ed 100644
--- a/src/proto_016_PtMumbai/lib_delegate/test/tenderbrute/tenderbrute_main.ml
+++ b/src/proto_016_PtMumbai/lib_delegate/test/tenderbrute/tenderbrute_main.ml
@@ -49,7 +49,7 @@ let delegate_encoding =
       case
         ~title:"Public key hash"
         (Tag 0)
-        Tezos_crypto.Signature.Public_key_hash.encoding
+        Signature.Public_key_hash.encoding
         (function `Pkh p -> Some p | _ -> None)
         (fun p -> `Pkh p);
       case
diff --git a/src/proto_016_PtMumbai/lib_delegate/test/test_scenario.ml b/src/proto_016_PtMumbai/lib_delegate/test/test_scenario.ml
index f10b60904c24c39e2620965ed7886a116c8d2744..cb34cc8d3d63e0d5f1f31c8ebfff437194229259 100644
--- a/src/proto_016_PtMumbai/lib_delegate/test/test_scenario.ml
+++ b/src/proto_016_PtMumbai/lib_delegate/test/test_scenario.ml
@@ -1,14 +1,14 @@
 open Mockup_simulator
 
-let bootstrap1 = Tezos_crypto.Signature.Public_key.hash bootstrap1
+let bootstrap1 = Signature.Public_key.hash bootstrap1
 
-let bootstrap2 = Tezos_crypto.Signature.Public_key.hash bootstrap2
+let bootstrap2 = Signature.Public_key.hash bootstrap2
 
-let bootstrap3 = Tezos_crypto.Signature.Public_key.hash bootstrap3
+let bootstrap3 = Signature.Public_key.hash bootstrap3
 
-let bootstrap4 = Tezos_crypto.Signature.Public_key.hash bootstrap4
+let bootstrap4 = Signature.Public_key.hash bootstrap4
 
-let bootstrap5 = Tezos_crypto.Signature.Public_key.hash bootstrap5
+let bootstrap5 = Signature.Public_key.hash bootstrap5
 
 let some_seed s = Some (Protocol.State_hash.of_b58check_exn s)
 
@@ -401,6 +401,14 @@ let test_scenario_f1 () =
   let d_proposed_l1_r1 = ref false in
   let a_proposed_l2_r0 = ref false in
   let stop_on_event0 _ = !a_proposed_l2_r0 in
+  let pass =
+    (* This is to be sure that the proposal for round r arrives while
+       the baker is in round r, and not in round r-1. (See related
+       issue:
+       https://gitlab.com/tezos/tezos/-/issues/4143). Otherwise, the
+       test does not perform as expected. *)
+    Delay 0.5
+  in
   let module Node_a_hooks : Hooks = struct
     include Default_hooks
 
@@ -416,7 +424,7 @@ let test_scenario_f1 () =
           (a_proposed_l2_r0 := true ;
            return_unit)
           >>=? fun () ->
-          return (block_hash, block_header, operations, [Pass; Pass; Pass; Pass])
+          return (block_hash, block_header, operations, [pass; pass; pass; pass])
       | _ ->
           failwith
             "unexpected injection on the node A, level = %ld / round = %ld"
@@ -455,7 +463,7 @@ let test_scenario_f1 () =
           (c_proposed_l1_r0 := true ;
            return_unit)
           >>=? fun () ->
-          return (block_hash, block_header, operations, [Pass; Pass; Pass; Pass])
+          return (block_hash, block_header, operations, [pass; pass; pass; pass])
       | _ ->
           failwith
             "unexpected injection on the node C, level = %ld / round = %ld"
@@ -484,7 +492,7 @@ let test_scenario_f1 () =
           (d_proposed_l1_r1 := true ;
            return_unit)
           >>=? fun () ->
-          return (block_hash, block_header, operations, [Pass; Pass; Pass; Pass])
+          return (block_hash, block_header, operations, [pass; pass; pass; pass])
       | _ ->
           failwith
             "unexpected injection on the node D, level = %ld / round = %ld"
@@ -1465,8 +1473,7 @@ let tests =
     tztest "scenario t1" `Quick test_scenario_t1;
     tztest "scenario t2" `Quick test_scenario_t2;
     tztest "scenario t3" `Quick test_scenario_t3;
-    (* See issue https://gitlab.com/nomadic-labs/tezos/-/issues/518 *)
-    (* tztest "scenario f1" `Quick test_scenario_f1; *)
+    tztest "scenario f1" `Quick test_scenario_f1;
     tztest "scenario f2" `Quick test_scenario_f2;
     tztest "scenario m1" `Quick test_scenario_m1;
     tztest "scenario m2" `Quick test_scenario_m2;