diff --git a/middle_end/flambda/lifting/sort_lifted_constants.ml b/middle_end/flambda/lifting/sort_lifted_constants.ml
index f79aa03a44fe..b42c9a0b7190 100644
--- a/middle_end/flambda/lifting/sort_lifted_constants.ml
+++ b/middle_end/flambda/lifting/sort_lifted_constants.ml
@@ -18,11 +18,43 @@
 
 open! Simplify_import
 
-module SCC_lifted_constants = Strongly_connected_components.Make (CIS)
+(* Sort code IDs and symbols by linkage name because ids are unstable. In
+   particular, if we sort by integer id as usual, expect tests can fail
+   because the roundtrip to .flt can change ids, which then changes the order
+   of the bindings. *)
+module CIS_by_name = struct
+  type t = Linkage_name.t * CIS.t
+
+  include Identifiable.Make (struct
+    type nonrec t = t
+
+    let compare (name1, _) (name2, _) = Linkage_name.compare name1 name2
+    let equal (name1, _) (name2, _) = Linkage_name.equal name1 name2
+    let print ppf (_name, cis) = CIS.print ppf cis
+    let output out (_name, cis) = CIS.output out cis
+    let hash (name, _) = Linkage_name.hash name
+  end)
+
+  let code_id code_id : t =
+    Symbol.linkage_name (Code_id.code_symbol code_id), Code_id code_id
+
+  let symbol symbol : t =
+    Symbol.linkage_name symbol, Symbol symbol
+
+  let of_ (cis : CIS.t) =
+    match cis with
+    | Code_id c -> code_id c
+    | Symbol s -> symbol s
+
+  let set_of_unordered_set set =
+    set |> CIS.Set.to_seq |> Seq.map of_ |> Set.of_seq
+end
+
+module SCC_lifted_constants = Strongly_connected_components.Make (CIS_by_name)
 
 let build_dep_graph lifted_constants =
   (* Format.eprintf "SORTING:\n%!"; *)
-  LCS.fold lifted_constants ~init:(CIS.Map.empty, CIS.Map.empty)
+  LCS.fold lifted_constants ~init:(CIS_by_name.Map.empty, CIS_by_name.Map.empty)
     ~f:(fun (dep_graph, code_id_or_symbol_to_const) lifted_constant ->
       (* Format.eprintf "One constant: %a\n%!" LC.print lifted_constant; *)
       ListLabels.fold_left (LC.definitions lifted_constant)
@@ -52,16 +84,20 @@ let build_dep_graph lifted_constants =
           let deps =
             CIS.Set.union (CIS.set_of_symbol_set free_syms)
               (CIS.set_of_code_id_set free_code_ids)
+            |> CIS_by_name.set_of_unordered_set
           in
           let being_defined =
             D.bound_symbols definition
             |> Bound_symbols.everything_being_defined
+            |> CIS_by_name.set_of_unordered_set
           in
-          CIS.Set.fold
+          CIS_by_name.Set.fold
             (fun being_defined (dep_graph, code_id_or_symbol_to_const) ->
-              let dep_graph = CIS.Map.add being_defined deps dep_graph in
+              let dep_graph =
+                CIS_by_name.Map.add being_defined deps dep_graph
+              in
               let code_id_or_symbol_to_const =
-                CIS.Map.add being_defined lifted_constant
+                CIS_by_name.Map.add being_defined lifted_constant
                   code_id_or_symbol_to_const
               in
               dep_graph, code_id_or_symbol_to_const)
@@ -78,7 +114,7 @@ let sort0 lifted_constants =
   in
   (*
   Format.eprintf "SCC graph is:@ %a\n%!"
-    (CIS.Map.print CIS.Set.print)
+    (CIS_by_name.Map.print CIS_by_name.Set.print)
     lifted_constants_dep_graph;
   *)
   let innermost_first =
@@ -92,12 +128,12 @@ let sort0 lifted_constants =
         in
         let _, lifted_constants =
           ListLabels.fold_left code_id_or_symbols
-            ~init:(CIS.Set.empty, [])
+            ~init:(CIS_by_name.Set.empty, [])
             ~f:(fun ((already_seen, definitions) as acc) code_id_or_symbol ->
-              if CIS.Set.mem code_id_or_symbol already_seen then acc
+              if CIS_by_name.Set.mem code_id_or_symbol already_seen then acc
               else
                 let lifted_constant =
-                  CIS.Map.find code_id_or_symbol code_id_or_symbol_to_const
+                  CIS_by_name.Map.find code_id_or_symbol code_id_or_symbol_to_const
                 in
                 let already_seen =
                   (* We may encounter the same defining expression more
@@ -105,8 +141,9 @@ let sort0 lifted_constants =
                      may bind more than one symbol.  We must avoid
                      duplicates in the resulting [LC.t]. *)
                   let bound_symbols = LC.bound_symbols lifted_constant in
-                  CIS.Set.union
-                    (Bound_symbols.everything_being_defined bound_symbols)
+                  CIS_by_name.Set.union
+                    (Bound_symbols.everything_being_defined bound_symbols
+                     |> CIS_by_name.set_of_unordered_set)
                     already_seen
                 in
                 already_seen, lifted_constant :: definitions)