diff --git a/middle_end/flambda/simplify/simplify_expr.ml b/middle_end/flambda/simplify/simplify_expr.ml
index 34c9c4fc7526..5613172b1aa7 100644
--- a/middle_end/flambda/simplify/simplify_expr.ml
+++ b/middle_end/flambda/simplify/simplify_expr.ml
@@ -37,6 +37,7 @@ let rec simplify_expr dacc expr ~down_to_up =
     Simplify_apply_cont_expr.simplify_apply_cont dacc apply_cont ~down_to_up
   | Switch switch ->
     Simplify_switch_expr.simplify_switch ~simplify_let dacc switch ~down_to_up
+      ~original_expr:expr
   | Invalid _ ->
     (* CR mshinwell: Make sure that a program can be simplified to just
        [Invalid].  [Un_cps] should translate any [Invalid] that it sees as if
diff --git a/middle_end/flambda/simplify/simplify_switch_expr.ml b/middle_end/flambda/simplify/simplify_switch_expr.ml
index 05b9135e5715..2b25c6952119 100644
--- a/middle_end/flambda/simplify/simplify_switch_expr.ml
+++ b/middle_end/flambda/simplify/simplify_switch_expr.ml
@@ -18,8 +18,8 @@
 
 open! Simplify_import
 
-let rebuild_switch ~simplify_let dacc ~arms ~scrutinee ~scrutinee_ty uacc
-      ~after_rebuild =
+let rebuild_switch ~arms ~scrutinee ~scrutinee_ty
+      ~tagged_scrutinee ~not_scrutinee uacc ~after_rebuild =
   let new_let_conts, arms, identity_arms, not_arms =
     Target_imm.Map.fold
       (fun arm (action, use_id, arity)
@@ -141,38 +141,6 @@ let rebuild_switch ~simplify_let dacc ~arms ~scrutinee ~scrutinee_ty uacc
       |> Continuation.Set.of_list
       |> Continuation.Set.get_singleton
   in
-  let create_tagged_scrutinee uacc dest ~make_body =
-    (* A problem with using [simplify_let] below is that the continuation
-       [dest] might have [Apply_cont_rewrite]s in the environment, left over
-       from the simplification of the existing uses.  We must clear these to
-       avoid a lookup failure for our new [Apply_cont] when
-       [Simplify_apply_cont] tries to rewrite the use.  There is no need for
-       the rewrites anyway; they have already been applied.
-       Likewise, we need to clear the continuation uses environment for
-       [dest] in [dacc], since our new [Apply_cont] might not match the
-       original uses (e.g. if a parameter has been removed). *)
-    let uacc =
-      UA.map_uenv uacc ~f:(fun uenv ->
-        UE.delete_apply_cont_rewrite uenv dest)
-    in
-    let dacc = DA.delete_continuation_uses dacc dest in
-    let bound_to = Variable.create "tagged_scrutinee" in
-    let body = make_body ~tagged_scrutinee:(Simple.var bound_to) in
-    let bound_to = Var_in_binding_pos.create bound_to NM.normal in
-    let defining_expr =
-      Named.create_prim (Unary (Box_number Untagged_immediate, scrutinee))
-        Debuginfo.none
-    in
-    let let_expr =
-      Let.create (Bindable_let_bound.singleton bound_to)
-        defining_expr
-        ~body
-        ~free_names_of_body:Unknown
-    in
-    simplify_let dacc let_expr
-      ~down_to_up:(fun _dacc ~rebuild ->
-        rebuild uacc ~after_rebuild:(fun expr uacc -> expr, uacc))
-  in
   (* CR mshinwell: Here and elsewhere [UA.name_occurrences] should be empty
      (maybe except for closure vars? -- check).  We should add asserts. *)
   let body, uacc =
@@ -185,37 +153,29 @@ let rebuild_switch ~simplify_let dacc ~arms ~scrutinee ~scrutinee_ty uacc
       let dbg = Debuginfo.none in
       match switch_is_identity with
       | Some dest ->
+        let apply_cont = Apply_cont.create dest ~args:[tagged_scrutinee] ~dbg in
+        let uacc =
+          UA.map_uenv uacc ~f:(fun uenv ->
+            UE.delete_apply_cont_rewrite uenv dest)
+        in
         let uacc =
-          UA.notify_removed ~operation:Removed_operations.branch uacc
+          UA.add_free_names uacc (Apply_cont.free_names apply_cont) |>
+          UA.notify_removed ~operation:Removed_operations.branch
         in
-        create_tagged_scrutinee uacc dest ~make_body:(fun ~tagged_scrutinee ->
-          (* No need to increment the cost_metrics inside [create_tagged_scrutinee] as it
-             will call simplify over the result of [make_body]. *)
-          Apply_cont.create dest ~args:[tagged_scrutinee] ~dbg
-          |> Expr.create_apply_cont)
+        Rebuilt_expr.create_apply_cont apply_cont, uacc
       | None ->
         match switch_is_boolean_not with
         | Some dest ->
+          let apply_cont = Apply_cont.create dest ~args:[not_scrutinee] ~dbg in
           let uacc =
-            UA.notify_removed ~operation:Removed_operations.branch uacc
+            UA.map_uenv uacc ~f:(fun uenv ->
+              UE.delete_apply_cont_rewrite uenv dest)
           in
-          create_tagged_scrutinee uacc dest ~make_body:(fun ~tagged_scrutinee ->
-            let not_scrutinee = Variable.create "not_scrutinee" in
-            let not_scrutinee' = Simple.var not_scrutinee in
-            let do_tagging =
-              Named.create_prim (P.Unary (Boolean_not, tagged_scrutinee))
-                Debuginfo.none
-            in
-            let bound =
-              VB.create not_scrutinee NM.normal
-              |> Bindable_let_bound.singleton
-            in
-            let body =
-              Apply_cont.create dest ~args:[not_scrutinee'] ~dbg
-              |> Expr.create_apply_cont
-            in
-            Let.create bound do_tagging ~body ~free_names_of_body:Unknown
-            |> Expr.create_let)
+          let uacc =
+            UA.add_free_names uacc (Apply_cont.free_names apply_cont) |>
+            UA.notify_removed ~operation:Removed_operations.branch
+          in
+          Rebuilt_expr.create_apply_cont apply_cont, uacc
         | None ->
           (* In that case, even though some branches were removed by simplify we
              should not count them in the number of removed operations: these
@@ -258,13 +218,10 @@ let rebuild_switch ~simplify_let dacc ~arms ~scrutinee ~scrutinee_ty uacc
   in
   after_rebuild expr uacc
 
-let simplify_switch ~simplify_let dacc switch ~down_to_up =
+let simplify_switch_aux ~scrutinee ~scrutinee_ty
+      ~tagged_scrutinee ~not_scrutinee
+      dacc switch ~down_to_up =
   let module AC = Apply_cont in
-  let scrutinee = Switch.scrutinee switch in
-  let scrutinee_ty =
-    S.simplify_simple dacc scrutinee ~min_name_mode:NM.normal
-  in
-  let scrutinee = T.get_alias_exn scrutinee_ty in
   let arms, dacc =
     let typing_env_at_use = DA.typing_env dacc in
     Target_imm.Map.fold (fun arm action (arms, dacc) ->
@@ -306,5 +263,77 @@ let simplify_switch ~simplify_let dacc switch ~down_to_up =
       (Target_imm.Map.empty, dacc)
     in
     down_to_up dacc
-      ~rebuild:(rebuild_switch ~simplify_let dacc ~arms ~scrutinee
-        ~scrutinee_ty)
+      ~rebuild:(rebuild_switch ~arms ~scrutinee
+        ~scrutinee_ty ~tagged_scrutinee ~not_scrutinee)
+
+let simplify_switch ~simplify_let ~original_expr dacc switch ~down_to_up =
+  let scrutinee = Switch.scrutinee switch in
+  let scrutinee_ty =
+    S.simplify_simple dacc scrutinee ~min_name_mode:NM.normal
+  in
+  let scrutinee = T.get_alias_exn scrutinee_ty in
+  let find_cse_simple prim =
+    (* prim is either boolean not or tagging of non constant values *)
+    let with_fixed_value = P.Eligible_for_cse.create_exn prim in
+    match DE.find_cse (DA.denv dacc) with_fixed_value with
+    | None -> None
+    | Some simple ->
+      match
+        TE.get_canonical_simple_exn (DA.typing_env dacc) simple
+          ~min_name_mode:NM.normal
+          ~name_mode_of_existing_simple:NM.normal
+      with
+      | exception Not_found -> None
+      | simple -> Some simple
+  in
+  let create_def name prim =
+    let bound_to = Variable.create name in
+    let bound_to = Var_in_binding_pos.create bound_to NM.normal in
+    let defining_expr = Named.create_prim prim Debuginfo.none in
+    let let_expr =
+      Let.create (Bindable_let_bound.singleton bound_to)
+        defining_expr
+        ~body:original_expr
+        ~free_names_of_body:Unknown
+    in
+    simplify_let dacc let_expr ~down_to_up
+  in
+  let tag_prim = P.Unary (Box_number Untagged_immediate, scrutinee) in
+  Simple.pattern_match scrutinee
+    ~const:(fun const ->
+      match Reg_width_things.Const.descr const with
+      | Naked_immediate imm ->
+        let tagged_scrutinee =
+          Simple.const (Reg_width_things.Const.tagged_immediate imm)
+        in
+        let not_scrutinee =
+          let not_imm =
+            if Target_imm.equal imm Target_imm.zero then
+              Target_imm.one
+            else
+              (* If the scrutinee is neither zero nor one, this value
+                 won't be used *)
+              Target_imm.zero
+          in
+          Simple.const (Reg_width_things.Const.tagged_immediate not_imm)
+        in
+        simplify_switch_aux dacc switch ~down_to_up
+          ~tagged_scrutinee ~not_scrutinee
+          ~scrutinee ~scrutinee_ty
+      | Tagged_immediate _ | Naked_float _ | Naked_int32 _
+      | Naked_int64 _ | Naked_nativeint _ ->
+        Misc.fatal_errorf "Switch scrutinee is not a naked immediate: %a"
+          Simple.print scrutinee)
+    ~name:(fun _ ->
+      match find_cse_simple tag_prim with
+      | None ->
+        create_def "tagged_scrutinee" tag_prim
+      | Some tagged_scrutinee ->
+        let not_prim = P.Unary (Boolean_not, tagged_scrutinee) in
+        match find_cse_simple not_prim with
+        | None ->
+          create_def "not_scrutinee" not_prim
+        | Some not_scrutinee ->
+          simplify_switch_aux dacc switch ~down_to_up
+            ~tagged_scrutinee ~not_scrutinee
+            ~scrutinee ~scrutinee_ty)
diff --git a/middle_end/flambda/simplify/simplify_switch_expr.mli b/middle_end/flambda/simplify/simplify_switch_expr.mli
index 6d623783953a..c9af3559f259 100644
--- a/middle_end/flambda/simplify/simplify_switch_expr.mli
+++ b/middle_end/flambda/simplify/simplify_switch_expr.mli
@@ -18,4 +18,5 @@
 
 val simplify_switch
    : simplify_let:Flambda.Let.t Simplify_common.expr_simplifier
+  -> original_expr:Flambda.Expr.t
   -> Flambda.Switch.t Simplify_common.expr_simplifier