diff --git a/src/lib_gossipsub/gossipsub_intf.ml b/src/lib_gossipsub/gossipsub_intf.ml
index 350af6ec385f57ae33601352a6898218f1710e50..3612c9b97a4e7eb9a33176c0b092afaf54a89c80 100644
--- a/src/lib_gossipsub/gossipsub_intf.ml
+++ b/src/lib_gossipsub/gossipsub_intf.ml
@@ -409,6 +409,13 @@ module type SCORE = sig
   include PRINTABLE with type t := t
 
   val pp_value : Format.formatter -> value -> unit
+
+  module Internal_for_tests : sig
+    val get_topic_params :
+      ('topic, 'span) score_parameters ->
+      'topic ->
+      'span per_topic_score_parameters
+  end
 end
 
 module type AUTOMATON = sig
diff --git a/src/lib_gossipsub/peers_score.ml b/src/lib_gossipsub/peers_score.ml
index 6ad3e338a803f5af86c0ad4e1ee2d41427aa503f..3f4906d0875a9601c129b4f66795ac6411f7fbaa 100644
--- a/src/lib_gossipsub/peers_score.ml
+++ b/src/lib_gossipsub/peers_score.ml
@@ -522,4 +522,8 @@ struct
       ]
 
   let pp_value = Fmt.float
+
+  module Internal_for_tests = struct
+    let get_topic_params = get_topic_params
+  end
 end
diff --git a/src/lib_gossipsub/test/test_gossipsub_shared.ml b/src/lib_gossipsub/test/test_gossipsub_shared.ml
index 4a75519721f06bef06e878dfba53e573d1218b0b..0c7f21a3544632c564280d1c7ec9a601d2dbe826 100644
--- a/src/lib_gossipsub/test/test_gossipsub_shared.ml
+++ b/src/lib_gossipsub/test/test_gossipsub_shared.ml
@@ -36,6 +36,8 @@ module Milliseconds = struct
 
   let of_int_s n = {ms = n * 1000}
 
+  let to_int_ms {ms} = ms
+
   let zero = {ms = 0}
 
   let add m1 m2 = of_int_ms (m1.ms + m2.ms)
@@ -63,6 +65,8 @@ module Milliseconds = struct
 
     let to_int_s = to_int_s
 
+    let to_int_ms = to_int_ms
+
     let to_float_s = to_float_s
 
     let of_int_s = of_int_s
@@ -94,9 +98,9 @@ module Time = struct
 
   let now () = !t
 
-  let elapse s =
-    assert (s >= 0) ;
-    t := Milliseconds.add !t (Milliseconds.of_int_s s)
+  let elapse ms =
+    assert (Milliseconds.(ms >= zero)) ;
+    t := Milliseconds.add !t ms
 
   let set now = t := now
 
diff --git a/src/lib_gossipsub/test/test_unit.ml b/src/lib_gossipsub/test/test_unit.ml
index 47ca42fcb4d0a92045346d0e16fecf72cb86cd24..7fd637b1d0c813250bdadb007aa8fabf04d9efd3 100644
--- a/src/lib_gossipsub/test/test_unit.ml
+++ b/src/lib_gossipsub/test/test_unit.ml
@@ -946,7 +946,7 @@ let test_do_not_graft_within_backoff_period rng limits parameters =
     |> WithExceptions.Result.get_ok ~loc:__LOC__
     |> List.fold_left
          (fun state i ->
-           Time.elapse 1 ;
+           Time.elapse @@ Milliseconds.of_int_s 1 ;
            Log.info "%d time tick(s) elapsed..." i ;
            let state, Heartbeat {to_graft; _} = GS.heartbeat state in
            let grafts = Peer.Map.bindings to_graft in
@@ -960,7 +960,7 @@ let test_do_not_graft_within_backoff_period rng limits parameters =
   in
   (* After elapsing one more second,
      the backoff should be cleared and the graft should be emitted. *)
-  Time.elapse 1 ;
+  Time.elapse @@ Milliseconds.of_int_s 1 ;
   let _state, Heartbeat {to_graft; _} = GS.heartbeat state in
   let grafts = Peer.Map.bindings to_graft in
   Check.((List.length grafts = 1) int ~error_msg:"Expected %R, got %L" ~__LOC__) ;
@@ -978,20 +978,40 @@ let test_unsubscribe_backoff rng limits parameters =
     ~tags:["gossipsub"; "heartbeat"; "join"; "leave"]
   @@ fun () ->
   let topic = "topic" in
+  let per_topic_score_parameters =
+    GS.Score.Internal_for_tests.get_topic_params limits.score_parameters topic
+  in
+  let mesh_message_deliveries_activation =
+    per_topic_score_parameters.mesh_message_deliveries_activation
+  in
   (* Only one peer => mesh too small and will try to regraft as early as possible *)
   let peers = make_peers ~number:1 in
+  (* Number of ticks until the unsubscribe backoff expires. *)
+  let backoff_ticks = 5 in
+  (* We must set [heartbeat_interval] so that
+     number_of_heartbeats_in_the_test * [heartbeat_interval] < [mesh_message_deliveries_activation]
+     holds. This prevents surpassing [mesh_message_deliveries_activation] within the test,
+     thus avoiding the activation of p3 penalty. Since number_of_heartbeats_in_the_test
+     is [backoff_ticks + 2], we set [heartbeat_interval] as the following.*)
+  let heartbeat_interval =
+    (Milliseconds.to_int_ms mesh_message_deliveries_activation - 1)
+    / (backoff_ticks + 2)
+    |> Milliseconds.of_int_ms
+  in
+  (* Time required until unsubscribe backoff expires. *)
+  let unsubscribe_backoff =
+    Milliseconds.(of_int_ms @@ (backoff_ticks * to_int_ms heartbeat_interval))
+  in
   let state =
     init_state
       ~rng
       ~limits:
         {
           limits with
+          heartbeat_interval;
           (* Run backoff clearing on every heartbeat tick. *)
           backoff_cleanup_ticks = 1;
-          (* We will run the heartbeat tick on each time tick to simplify the test. *)
-          heartbeat_interval = Milliseconds.of_int_s 1;
-          (* Set unsubscribe backoff to 5. *)
-          unsubscribe_backoff = Milliseconds.of_int_s 5;
+          unsubscribe_backoff;
         }
       ~parameters
       ~peers
@@ -1002,14 +1022,14 @@ let test_unsubscribe_backoff rng limits parameters =
   (* Peer unsubscribes then subscribes from topic. *)
   let state, _ = GS.leave {topic} state in
   let state, _ = GS.join {topic} state in
-  (* No graft should be emitted until 7 time ticks pass.
-     The additional 2 time ticks from the backoff is due to the "backoff slack". *)
+  (* No graft should be emitted until [(backoff_ticks + 2) * heartbeat_interval] elapse.
+     The additional 2 [heartbeat_interval] is due to the "backoff slack". *)
   let state =
-    List.init ~when_negative_length:() 6 (fun i -> i + 1)
+    List.init ~when_negative_length:() (backoff_ticks + 1) (fun i -> i + 1)
     |> WithExceptions.Result.get_ok ~loc:__LOC__
     |> List.fold_left
          (fun state i ->
-           Time.elapse 1 ;
+           Time.elapse @@ heartbeat_interval ;
            Log.info "%d time tick(s) elapsed..." i ;
            let state, Heartbeat {to_graft; _} = GS.heartbeat state in
            let grafts = Peer.Map.bindings to_graft in
@@ -1021,9 +1041,9 @@ let test_unsubscribe_backoff rng limits parameters =
            state)
          state
   in
-  (* After elapsing one more second,
+  (* After elapsing one more [heartbeat_interval],
      the backoff should be cleared and the graft should be emitted. *)
-  Time.elapse 1 ;
+  Time.elapse @@ heartbeat_interval ;
   let _state, Heartbeat {to_graft; _} = GS.heartbeat state in
   let grafts = Peer.Map.bindings to_graft in
   Check.((List.length grafts = 1) int ~error_msg:"Expected %R, got %L" ~__LOC__) ;
diff --git a/src/lib_gossipsub/tezos_gossipsub.ml b/src/lib_gossipsub/tezos_gossipsub.ml
index 2ece1d7a37808513e00b6f00346807c9cbd597a4..34b4f907a5f55995b4d00b3a76700f16c0fa7329 100644
--- a/src/lib_gossipsub/tezos_gossipsub.ml
+++ b/src/lib_gossipsub/tezos_gossipsub.ml
@@ -1110,6 +1110,15 @@ module Make (C : AUTOMATON_CONFIG) :
           in
           return (Peer.Set.union more_peers valid_fanout_peers)
       in
+      (* Notify scoring about the graft. *)
+      let scores =
+        Peer.Set.fold
+          (fun peer scores ->
+            update_scores_score peer (fun s -> Score.graft s topic) scores)
+          peers
+          scores
+      in
+      let* () = set_scores scores in
       let* () = set_mesh_topic topic peers in
       let* () = delete_fanout topic in
       Joining_topic {to_graft = peers} |> return
@@ -1608,6 +1617,16 @@ module Make (C : AUTOMATON_CONFIG) :
           backoff
         |> set_backoff
       in
+      (* Notify scoring about the grafts. *)
+      let scores =
+        Peer.Map.fold
+          (fun peer ->
+            Topic.Set.fold (fun topic ->
+                update_scores_score peer (fun s -> Score.graft s topic)))
+          to_graft
+          scores
+      in
+      let* () = set_scores scores in
       (* Update mesh for grafted and pruned peers *)
       let* () = update_mesh mesh ~to_graft ~to_prune in
       return (to_graft, to_prune, noPX_peers)