diff --git a/docs/protocols/alpha.rst b/docs/protocols/alpha.rst
index f21a888a4f230e1514d779460779ec40b11eb53f..c5a91dd8947ad044bef78b9914bcb85f4b278e2f 100644
--- a/docs/protocols/alpha.rst
+++ b/docs/protocols/alpha.rst
@@ -34,6 +34,10 @@ Smart Rollups
   of indiscriminately imposing them (e.g., imposing 2 weeks for the challenge
   window or 15 minutes for the commitment period). (MR :gl:`!13821`)
 
+- Fixed the traversal logic of the commitments tree, by considering previous
+  commitment periods when computing what should be the level of a commitment
+  successor. (MR :gl:`!13841`)
+
 Zero Knowledge Rollups (ongoing)
 --------------------------------
 
diff --git a/src/proto_alpha/lib_protocol/TEZOS_PROTOCOL b/src/proto_alpha/lib_protocol/TEZOS_PROTOCOL
index d79b763f6783e06badd6eaeb23ea865e3c00557d..feea36bc792cf2ca5aab3ac5c7d61bfa35210b52 100644
--- a/src/proto_alpha/lib_protocol/TEZOS_PROTOCOL
+++ b/src/proto_alpha/lib_protocol/TEZOS_PROTOCOL
@@ -206,8 +206,8 @@
         "Sc_rollup_commitment_storage",
         "Sc_rollup_outbox_storage",
         "Sc_rollup_whitelist_storage",
-        "Sc_rollup_stake_storage",
         "Sc_rollup_storage",
+        "Sc_rollup_stake_storage",
         "Dal_slot_storage",
         "Sc_rollup_refutation_storage",
         "Zk_rollup_errors",
diff --git a/src/proto_alpha/lib_protocol/dune b/src/proto_alpha/lib_protocol/dune
index 2813d1b0f37451a2b219483f9a1412bc8b01b828..fede92899f904a47b1d01f1940670cf5b494471b 100644
--- a/src/proto_alpha/lib_protocol/dune
+++ b/src/proto_alpha/lib_protocol/dune
@@ -218,8 +218,8 @@
   Sc_rollup_commitment_storage
   Sc_rollup_outbox_storage
   Sc_rollup_whitelist_storage
-  Sc_rollup_stake_storage
   Sc_rollup_storage
+  Sc_rollup_stake_storage
   Dal_slot_storage
   Sc_rollup_refutation_storage
   Zk_rollup_errors
@@ -518,8 +518,8 @@
   sc_rollup_commitment_storage.ml sc_rollup_commitment_storage.mli
   sc_rollup_outbox_storage.ml sc_rollup_outbox_storage.mli
   sc_rollup_whitelist_storage.ml sc_rollup_whitelist_storage.mli
-  sc_rollup_stake_storage.ml sc_rollup_stake_storage.mli
   sc_rollup_storage.ml sc_rollup_storage.mli
+  sc_rollup_stake_storage.ml sc_rollup_stake_storage.mli
   dal_slot_storage.ml dal_slot_storage.mli
   sc_rollup_refutation_storage.ml sc_rollup_refutation_storage.mli
   zk_rollup_errors.ml
@@ -819,8 +819,8 @@
   sc_rollup_commitment_storage.ml sc_rollup_commitment_storage.mli
   sc_rollup_outbox_storage.ml sc_rollup_outbox_storage.mli
   sc_rollup_whitelist_storage.ml sc_rollup_whitelist_storage.mli
-  sc_rollup_stake_storage.ml sc_rollup_stake_storage.mli
   sc_rollup_storage.ml sc_rollup_storage.mli
+  sc_rollup_stake_storage.ml sc_rollup_stake_storage.mli
   dal_slot_storage.ml dal_slot_storage.mli
   sc_rollup_refutation_storage.ml sc_rollup_refutation_storage.mli
   zk_rollup_errors.ml
@@ -1104,8 +1104,8 @@
   sc_rollup_commitment_storage.ml sc_rollup_commitment_storage.mli
   sc_rollup_outbox_storage.ml sc_rollup_outbox_storage.mli
   sc_rollup_whitelist_storage.ml sc_rollup_whitelist_storage.mli
-  sc_rollup_stake_storage.ml sc_rollup_stake_storage.mli
   sc_rollup_storage.ml sc_rollup_storage.mli
+  sc_rollup_stake_storage.ml sc_rollup_stake_storage.mli
   dal_slot_storage.ml dal_slot_storage.mli
   sc_rollup_refutation_storage.ml sc_rollup_refutation_storage.mli
   zk_rollup_errors.ml
diff --git a/src/proto_alpha/lib_protocol/init_storage.ml b/src/proto_alpha/lib_protocol/init_storage.ml
index 245659ae08f1a55fba9ca1a627e60f8f5e9102b3..04a32a02a4db93217da416baf854db79418e02e2 100644
--- a/src/proto_alpha/lib_protocol/init_storage.ml
+++ b/src/proto_alpha/lib_protocol/init_storage.ml
@@ -112,9 +112,21 @@ let patch_script ctxt (address, hash, patched_code) =
 let prepare_first_block chain_id ctxt ~typecheck_smart_contract
     ~typecheck_smart_rollup ~level ~timestamp ~predecessor =
   let open Lwt_result_syntax in
-  let* previous_protocol, _previous_proto_constants, ctxt =
+  let* previous_protocol, previous_proto_constants, ctxt =
     Raw_context.prepare_first_block ~level ~timestamp chain_id ctxt
   in
+  let*? level = Raw_level_repr.of_int32 level in
+  (* To gracefully handle time block change, we keep a record of all commitment
+     periods used in the past. *)
+  let* ctxt =
+    match previous_proto_constants with
+    | Some previous_proto_constants ->
+        Sc_rollup_storage.save_commitment_period
+          ctxt
+          previous_proto_constants.sc_rollup.commitment_period_in_blocks
+          level
+    | None -> return ctxt
+  in
   let parametric = Raw_context.constants ctxt in
   let*! ctxt =
     let*! ctxt =
@@ -128,7 +140,6 @@ let prepare_first_block chain_id ctxt ~typecheck_smart_contract
     match previous_protocol with
     | Genesis param ->
         (* This is the genesis protocol: initialise the state *)
-        let*? level = Raw_level_repr.of_int32 level in
         let* ctxt =
           Storage.Tenderbake.First_level_of_protocol.init ctxt level
         in
@@ -191,7 +202,6 @@ let prepare_first_block chain_id ctxt ~typecheck_smart_contract
            if that is done, do not set Storage.Tenderbake.First_level_of_protocol.
            /!\ this storage is also use to add the smart rollup
                inbox migration message. see `sc_rollup_inbox_storage`. *)
-        let*? level = Raw_level_repr.of_int32 level in
         let* ctxt =
           Storage.Tenderbake.First_level_of_protocol.update ctxt level
         in
diff --git a/src/proto_alpha/lib_protocol/sc_rollup_repr.ml b/src/proto_alpha/lib_protocol/sc_rollup_repr.ml
index 9dae544442515647796a6c4a39b62b7f7ac28e13..fa3b8cc822639f38ecb461eb789d6b83c494bd9c 100644
--- a/src/proto_alpha/lib_protocol/sc_rollup_repr.ml
+++ b/src/proto_alpha/lib_protocol/sc_rollup_repr.ml
@@ -106,3 +106,21 @@ module Number_of_ticks = struct
     | Some zero -> zero
     | None -> assert false (* unreachable case, since [min_int = 0l] *)
 end
+
+module Past_commitment_period = struct
+  type t = {
+    commitment_period_in_blocks : int;
+    next_protocol_activation : Raw_level_repr.t;
+  }
+
+  let encoding =
+    Data_encoding.(
+      conv
+        (fun {commitment_period_in_blocks; next_protocol_activation} ->
+          (commitment_period_in_blocks, next_protocol_activation))
+        (fun (commitment_period_in_blocks, next_protocol_activation) ->
+          {commitment_period_in_blocks; next_protocol_activation})
+      @@ obj2
+           (req "commitment_period" int31)
+           (req "next_protocol_activation" Raw_level_repr.encoding))
+end
diff --git a/src/proto_alpha/lib_protocol/sc_rollup_repr.mli b/src/proto_alpha/lib_protocol/sc_rollup_repr.mli
index d4d6aa0dcbfb8687d560414a09a87734a8e79889..576fdcb8cd267d861c7ca2a8cbe4ea5ff9560ca0 100644
--- a/src/proto_alpha/lib_protocol/sc_rollup_repr.mli
+++ b/src/proto_alpha/lib_protocol/sc_rollup_repr.mli
@@ -100,3 +100,23 @@ end
 
 (** The data model uses an index of these addresses. *)
 module Index : Storage_description.INDEX with type t = Address.t
+
+module Past_commitment_period : sig
+  type t = {
+    commitment_period_in_blocks : int;
+        (** The number of blocks separating two valid commitment for a given
+            particular Tezos protocol. *)
+    next_protocol_activation : Raw_level_repr.t;
+        (** The activation level of the next protocol, which is also the last
+            level during which the commitment period is valid. That is, if
+
+            {math inbox_level + commitment_period_in_blocks <= next_protocol_activation}
+
+            then [inbox_level + commitment_period_in_blocks] is the expected
+            level of the next commitment.
+
+            Otherwise, the commitment period of the next protocol applies. *)
+  }
+
+  val encoding : t Data_encoding.t
+end
diff --git a/src/proto_alpha/lib_protocol/sc_rollup_stake_storage.ml b/src/proto_alpha/lib_protocol/sc_rollup_stake_storage.ml
index c25546aecb4615ece6cb7fca28b579be4068a953..9e07240577eabf75fc0429d7b75f1d7ec51875c2 100644
--- a/src/proto_alpha/lib_protocol/sc_rollup_stake_storage.ml
+++ b/src/proto_alpha/lib_protocol/sc_rollup_stake_storage.ml
@@ -279,13 +279,12 @@ let assert_commitment_period ctxt rollup commitment =
   (* Commitments needs to be posted for inbox levels every [commitment_period].
      Therefore, [commitment.inbox_level] must be
      [predecessor_commitment.inbox_level + commitment_period]. *)
-  let sc_rollup_commitment_period =
-    Constants_storage.sc_rollup_commitment_period_in_blocks ctxt
+  let* expected_level =
+    Sc_rollup_storage.next_commitment_level ctxt pred_level
   in
   let* () =
     fail_unless
-      Raw_level_repr.(
-        commitment.inbox_level = add pred_level sc_rollup_commitment_period)
+      Raw_level_repr.(commitment.inbox_level = expected_level)
       Sc_rollup_bad_inbox_level
   in
   return ctxt
@@ -761,11 +760,8 @@ let cement_commitment ctxt rollup =
   let* old_lcc, old_lcc_level, ctxt =
     Commitment_storage.last_cemented_commitment_hash_with_level ctxt rollup
   in
-  let sc_rollup_commitment_period =
-    Constants_storage.sc_rollup_commitment_period_in_blocks ctxt
-  in
-  let new_lcc_level =
-    Raw_level_repr.add old_lcc_level sc_rollup_commitment_period
+  let* new_lcc_level =
+    Sc_rollup_storage.next_commitment_level ctxt old_lcc_level
   in
   (* Assert conditions to cement are met. *)
   let* ctxt, (new_lcc_commitment, new_lcc_commitment_hash), dangling_commitments
diff --git a/src/proto_alpha/lib_protocol/sc_rollup_storage.ml b/src/proto_alpha/lib_protocol/sc_rollup_storage.ml
index fe875fc9348351411791a0740bfc453e262d15cf..b5c2c16104a3aedb052e4ba0206985b053d650e1 100644
--- a/src/proto_alpha/lib_protocol/sc_rollup_storage.ml
+++ b/src/proto_alpha/lib_protocol/sc_rollup_storage.ml
@@ -224,3 +224,51 @@ let must_exist ctxt rollup =
   let open Lwt_result_syntax in
   let* ctxt, exists = Store.Genesis_info.mem ctxt rollup in
   if exists then return ctxt else tzfail (Sc_rollup_does_not_exist rollup)
+
+let get_past_commitment_periods ctxt =
+  let open Lwt_result_syntax in
+  let+ cell = Store.Past_commitment_periods.find ctxt in
+  Option.value ~default:[] cell
+
+let save_commitment_period ctxt previous_commitment_period
+    next_protocol_activation =
+  let open Lwt_result_syntax in
+  let* past_commitments = get_past_commitment_periods ctxt in
+  let*! ctxt =
+    Store.Past_commitment_periods.add
+      ctxt
+      (past_commitments
+      @ [
+          {
+            commitment_period_in_blocks = previous_commitment_period;
+            next_protocol_activation;
+          };
+        ])
+    (* We enforce the fact that the past commitment periods is sorted in
+       ascending order of [next_protocol_activation_level]. *)
+  in
+  return ctxt
+
+let next_commitment_level ctxt inbox_level =
+  let open Lwt_result_syntax in
+  (* This function assumes [past_commitments] is sorted in ascending order of
+     [next_protocol_activation_level]. This invariant is enforced by
+     [save_commitment_period]. *)
+  let+ past_commitments = get_past_commitment_periods ctxt in
+  let candidate_level =
+    List.find_map
+      (fun Sc_rollup_repr.Past_commitment_period.
+             {commitment_period_in_blocks; next_protocol_activation} ->
+        let candidate_level =
+          Raw_level_repr.add inbox_level commitment_period_in_blocks
+        in
+        if Raw_level_repr.(candidate_level <= next_protocol_activation) then
+          Some candidate_level
+        else None)
+      past_commitments
+  in
+  match candidate_level with
+  | Some candidate_level -> candidate_level
+  | None ->
+      Raw_level_repr.(
+        add inbox_level Raw_context.(sc_rollup ctxt).commitment_period_in_blocks)
diff --git a/src/proto_alpha/lib_protocol/sc_rollup_storage.mli b/src/proto_alpha/lib_protocol/sc_rollup_storage.mli
index 8da1651e5a5bd62f8612d3e17f4657a69b5d5479..ca6ac76a88a0eaa6ef43d351f8f4dde256a93d11 100644
--- a/src/proto_alpha/lib_protocol/sc_rollup_storage.mli
+++ b/src/proto_alpha/lib_protocol/sc_rollup_storage.mli
@@ -100,3 +100,19 @@ val parameters_type :
     returned. *)
 val must_exist :
   Raw_context.t -> Sc_rollup_repr.t -> Raw_context.t tzresult Lwt.t
+
+(** [save_commitment_period ctxt previous_commitment_period next_protocol_activation]
+    records that before level [next_protocol_activation], the commitment period
+    to use is [previous_commitment_period]. *)
+val save_commitment_period :
+  Raw_context.t -> int -> Raw_level_repr.t -> Raw_context.t tzresult Lwt.t
+
+(** [next_commitment_level ctxt inbox_level] returns the level that the next
+    commitment should target, taking into account the commitment periods of
+    past protocols as well as the current one.
+
+    {b Precondition:} For [next_commitment_level] result to actually be a
+    valid level for a commitment requires that [inbox_level] is a valid level
+    for a commitment as well. *)
+val next_commitment_level :
+  Raw_context.t -> Raw_level_repr.t -> Raw_level_repr.t tzresult Lwt.t
diff --git a/src/proto_alpha/lib_protocol/storage.ml b/src/proto_alpha/lib_protocol/storage.ml
index b1d0075db47f01a6142dd1304ad003bf4ee47335..bc307ee8fbcbceb7f6141b815eb0227a7946ce6e 100644
--- a/src/proto_alpha/lib_protocol/storage.ml
+++ b/src/proto_alpha/lib_protocol/storage.ml
@@ -1830,6 +1830,18 @@ module Sc_rollup = struct
         let encoding = Sc_rollup_commitment_repr.genesis_info_encoding
       end)
 
+  module Past_commitment_periods =
+    Make_single_data_storage (Registered) (Raw_context)
+      (struct
+        let name = ["past_commitment_periods"]
+      end)
+      (struct
+        type t = Sc_rollup_repr.Past_commitment_period.t list
+
+        let encoding =
+          Data_encoding.(list Sc_rollup_repr.Past_commitment_period.encoding)
+      end)
+
   module Inbox = struct
     include
       Make_single_data_storage (Registered) (Raw_context)
diff --git a/src/proto_alpha/lib_protocol/storage.mli b/src/proto_alpha/lib_protocol/storage.mli
index 12fbd3bccadd17fc6e8fbd793389ab364828f72a..f48967588c4291604a4d015e0e0bc0c5b230cab0 100644
--- a/src/proto_alpha/lib_protocol/storage.mli
+++ b/src/proto_alpha/lib_protocol/storage.mli
@@ -850,6 +850,11 @@ module Sc_rollup : sig
        and type value = Sc_rollup_commitment_repr.genesis_info
        and type t := Raw_context.t
 
+  module Past_commitment_periods :
+    Single_data_storage
+      with type value = Sc_rollup_repr.Past_commitment_period.t list
+       and type t := Raw_context.t
+
   module Inbox :
     Single_data_storage
       with type value = Sc_rollup_inbox_repr.t
diff --git a/tezt/tests/sc_rollup_migration.ml b/tezt/tests/sc_rollup_migration.ml
index 45110add747d2f8af0322fb73f8519f30fbf468c..61b24f9d7c35484e2062ed92f0cc415248a0fe8e 100644
--- a/tezt/tests/sc_rollup_migration.ml
+++ b/tezt/tests/sc_rollup_migration.ml
@@ -605,6 +605,95 @@ let test_rollup_node_catchup_migration ~kind ~migrate_from ~migrate_to =
     ~description
     ()
 
+let test_rollup_node_migration_constant_changes ~kind ~migrate_from ~migrate_to
+    =
+  let next_block client rollup_node =
+    let* () = Sc_rollup_helpers.send_messages 1 client in
+    let* _ = Sc_rollup_node.wait_sync ~timeout:10. rollup_node in
+    unit
+  in
+  let tags = ["constants_changes"] in
+  let description =
+    "node can deal with protocol migration with constant changes"
+  in
+  let commitment_period = 6 in
+  let challenge_window = 6 in
+  let scenario_prior ~sc_rollup:_ ~rollup_node _tezos_node tezos_client =
+    (* Bake enough blocks to compute *and* publish a commitment in the previous
+       protocol. *)
+    let* () =
+      repeat (commitment_period + 4) (fun () ->
+          next_block tezos_client rollup_node)
+    in
+    let* commitment_and_hash =
+      Sc_rollup_node.RPC.call
+        rollup_node
+        (Sc_rollup_rpc.get_global_last_stored_commitment ())
+    in
+    (* Check that the first commitment has been indeed computed by the rollup
+       node. *)
+    Check.(
+      (commitment_and_hash.commitment.inbox_level = 2 + commitment_period) int)
+      ~error_msg:
+        "Unexpected last stored commitment, got %L but was expecting %R" ;
+    unit
+  in
+  let scenario_after ~sc_rollup ~rollup_node tezos_node tezos_client () =
+    (* Fetch the new commitment period, after constants update *)
+    let* {commitment_period_in_blocks = new_commitment_period; _} =
+      Sc_rollup_helpers.get_sc_rollup_constants tezos_client
+    in
+    (* Bake twice commitment periods. This should be enough for the rollup node
+       to compute two more commitments in the next protocol, and to decide to
+       cement the first one. *)
+    let* () =
+      repeat (2 * new_commitment_period) (fun () ->
+          next_block tezos_client rollup_node)
+    in
+    (* We first check the last computed commitment. *)
+    let* commitment_and_hash =
+      Sc_rollup_node.RPC.call
+        rollup_node
+        (Sc_rollup_rpc.get_global_last_stored_commitment ())
+    in
+    Check.(
+      (commitment_and_hash.commitment.inbox_level
+      = 2 + commitment_period + (2 * new_commitment_period))
+        int)
+      ~error_msg:
+        "Unexpected last stored commitment, got %L but was expecting %R" ;
+    (* We bake a few more blocks, to ensure the rollup node indeed injects a
+       cementation operation. *)
+    let* () = repeat 3 (fun () -> next_block tezos_client rollup_node) in
+    (* We check the LCC is indeed at the expected level. *)
+    let* commitment =
+      Node.RPC.call
+        tezos_node
+        RPC.(
+          get_chain_block_context_smart_rollups_smart_rollup_last_cemented_commitment_hash_with_level
+            sc_rollup)
+    in
+    Check.(
+      (JSON.(commitment |-> "level" |> as_int)
+      = 2 + commitment_period + new_commitment_period)
+        int)
+      ~error_msg:
+        "Unexpected last cemented commitment, got %L but was expecting %R" ;
+    unit
+  in
+  test_l2_migration_scenario
+    ~with_constant_change:true
+    ~tags
+    ~kind
+    ~commitment_period
+    ~challenge_window
+    ~migrate_from
+    ~migrate_to
+    ~scenario_prior
+    ~scenario_after
+    ~description
+    ()
+
 (* Test originate rollup in previous protocol and start node in a different
    protocol. *)
 let test_originate_before_migration ~kind ~migrate_from ~migrate_to =
@@ -950,6 +1039,7 @@ let register_migration ~kind ~migrate_from ~migrate_to =
   test_cont_refute_pre_migration ~kind ~migrate_from ~migrate_to ;
   test_rollup_node_simple_migration ~kind ~migrate_from ~migrate_to ;
   test_rollup_node_catchup_migration ~kind ~migrate_from ~migrate_to ;
+  test_rollup_node_migration_constant_changes ~kind ~migrate_from ~migrate_to ;
   test_originate_before_migration ~kind ~migrate_from ~migrate_to ;
   test_migration_removes_dead_games ~kind ~migrate_from ~migrate_to