diff --git a/src/core/lwt_stream.ml b/src/core/lwt_stream.ml
index e5f6e05473..d39667540e 100644
--- a/src/core/lwt_stream.ml
+++ b/src/core/lwt_stream.ml
@@ -469,6 +469,22 @@ let rec get_exn_rec s node =
 
 let map_exn s = from (fun () -> get_exn_rec s s.node)
 
+let rec get_exn_rec' s node =
+  if node == !(s.last) then
+    Lwt.try_bind
+      (fun () -> feed s)
+      (fun () -> get_exn_rec' s node)
+      (fun exn -> Lwt.return (Some (Result.Error exn)))
+  else
+    match node.data with
+      | Some value ->
+          consume s node;
+          Lwt.return (Some (Result.Ok value))
+      | None ->
+          Lwt.return_none
+
+let wrap_exn s = from (fun () -> get_exn_rec' s s.node)
+
 let rec nget_rec node acc n s =
   if n <= 0 then
     Lwt.return (List.rev acc)
diff --git a/src/core/lwt_stream.mli b/src/core/lwt_stream.mli
index 4f89bda5ee..b68d6fd4b5 100644
--- a/src/core/lwt_stream.mli
+++ b/src/core/lwt_stream.mli
@@ -323,17 +323,12 @@ val concat : 'a t t -> 'a t
 val flatten : 'a list t -> 'a t
   (** [flatten st = map_list (fun l -> l) st] *)
 
-(** A value or an error. *)
-type 'a result =
-  | Value of 'a
-  | Error of exn
-
-val map_exn : 'a t -> 'a result t
-  (** [map_exn s] returns a stream that captures all exceptions raised
-      by the source of the stream (the function passed to {!from}).
+val wrap_exn : 'a t -> 'a Lwt.result t
+(** [wrap_exn s] is a stream [s'] such that each time [s] yields a value [v],
+    [s'] yields [Result.Ok v], and when the source of [s] raises an exception
+    [e], [s'] yields [Result.Error e].
 
-      Note that for push-streams (as returned by {!create}) all
-      elements of the mapped streams are values. *)
+    Note that push-streams (as returned by {!create}) never raise exceptions. *)
 
 (** {2 Parsing} *)
 
@@ -356,3 +351,28 @@ val hexdump : char t -> string t
         let () = Lwt_main.run (Lwt_io.write_lines Lwt_io.stdout (Lwt_stream.hexdump (Lwt_io.read_lines Lwt_io.stdin)))
       ]}
   *)
+
+(** {2 Deprecated} *)
+
+type 'a result =
+  | Value of 'a
+  | Error of exn
+  [@@ocaml.deprecated
+"This type is being replaced by Lwt.result and the corresponding function
+Lwt_stream.wrap_exn."]
+(** A value or an error.
+
+    @deprecated Replaced by {!wrap_exn}, which uses {!Lwt.result}. *)
+
+[@@@ocaml.warning "-3"]
+val map_exn : 'a t -> 'a result t
+  [@@ocaml.deprecated "Use Lwt_stream.wrap_exn"]
+(** [map_exn s] returns a stream that captures all exceptions raised
+    by the source of the stream (the function passed to {!from}).
+
+    Note that for push-streams (as returned by {!create}) all
+    elements of the mapped streams are values.
+
+    @deprecated Use {!wrap_exn}. *)
+
+[@@@ocaml.warning "+3"]
diff --git a/tests/core/test_lwt_stream.ml b/tests/core/test_lwt_stream.ml
index b4b9816f1c..ef21b5752a 100644
--- a/tests/core/test_lwt_stream.ml
+++ b/tests/core/test_lwt_stream.ml
@@ -276,7 +276,13 @@ let suite = suite "lwt_stream" [
        (* TODO: This will no longer be a shadowing open once Lwt_stream.error
           is removed. *)
        let open! Lwt_stream in
-       let l = [Value 1; Error Exit; Error (Failure "plop"); Value 42; Error End_of_file] in
+       let l =
+         [Result.Ok 1;
+          Result.Error Exit;
+          Result.Error (Failure "plop");
+          Result.Ok 42;
+          Result.Error End_of_file]
+       in
        let q = ref l in
        let stream =
          Lwt_stream.from
@@ -284,14 +290,14 @@ let suite = suite "lwt_stream" [
               match !q with
                 | [] ->
                     return None
-                | Value x :: l ->
+                | (Result.Ok x)::l ->
                     q := l;
                     return (Some x)
-                | Error e :: l ->
+                | (Result.Error e)::l ->
                     q := l;
                     Lwt.fail e)
        in
-       Lwt_stream.to_list (Lwt_stream.map_exn stream) >>= fun l' ->
+       Lwt_stream.to_list (Lwt_stream.wrap_exn stream) >>= fun l' ->
        return (l = l'));
 
   test "is_closed"