diff --git a/arrayjit/lib/backend_impl.ml b/arrayjit/lib/backend_impl.ml
index bafeda3..61de5d6 100644
--- a/arrayjit/lib/backend_impl.ml
+++ b/arrayjit/lib/backend_impl.ml
@@ -106,9 +106,10 @@ struct
       latest_stream_id = -1;
       released = Atomic.make false;
       cross_stream_candidates = Hashtbl.create (module Tnode);
-      owner_streams = Hashtbl.create (module Tnode);
-      writer_streams = Hashtbl.create (module Tnode);
-      reader_streams = Hashtbl.create (module Tnode);
+      owner_stream = Hashtbl.create (module Tnode);
+      shared_writer_streams = Hashtbl.create (module Tnode);
+      host_reading_streams = Hashtbl.create (module Tnode);
+      host_writing_streams = Hashtbl.create (module Tnode);
     }
 
   let make_stream device runner ~stream_id =
@@ -120,6 +121,7 @@ struct
       stream_id;
       allocated_buffer = None;
       updating_for = Hashtbl.create (module Tnode);
+      reader_streams = Hashtbl.create (module Tnode);
     }
 
   let get_name stream = [%string "%{name}:%{stream.device.ordinal#Int}:%{stream.stream_id#Int}"]
diff --git a/arrayjit/lib/backend_intf.ml b/arrayjit/lib/backend_intf.ml
index 5353d32..9a37a90 100644
--- a/arrayjit/lib/backend_intf.ml
+++ b/arrayjit/lib/backend_intf.ml
@@ -91,17 +91,23 @@ type ('buffer_ptr, 'dev, 'runner, 'event) device = {
   cross_stream_candidates : 'buffer_ptr Hashtbl.M(Tnode).t;
       (** Freshly created arrays that might be shared across streams. The map can both grow and
           shrink. *)
-  owner_streams : ('buffer_ptr, 'dev, 'runner, 'event) stream Hashtbl.M(Tnode).t;
-      (** The stream owning a given node. This map can only grow.
-
-          Currently, if the memory mode of a node is inferred, only this stream will modify a
-          cross-stream shared array. But memory modes can also be set manually. *)
-  writer_streams : (('buffer_ptr, 'dev, 'runner, 'event) stream * 'event) list Hashtbl.M(Tnode).t;
-      (** The streams that most recently have been scheduled to update (write to) the node, and the
-          associated update completion event. The completed events are removed opportunistically. *)
-  reader_streams : (('buffer_ptr, 'dev, 'runner, 'event) stream * 'event) list Hashtbl.M(Tnode).t;
-      (** The streams that most recently have been reading from the node, and the associated use
-          completion events. The completed events are removed opportunistically. *)
+  owner_stream : ('buffer_ptr, 'dev, 'runner, 'event) stream Hashtbl.M(Tnode).t;
+      (** The stream owning a given node. This map can only grow. Currently, if the memory mode of a
+          node is inferred, only this stream will modify a cross-stream shared array. But memory
+          modes can also be set manually. *)
+  shared_writer_streams :
+    (('buffer_ptr, 'dev, 'runner, 'event) stream * 'event) list Hashtbl.M(Tnode).t;
+      (** The streams that most recently have been scheduled to update (write to) a
+          cross-stream-shared node, and the associated update completion event. The completed events
+          are removed opportunistically. *)
+  host_reading_streams :
+    (('buffer_ptr, 'dev, 'runner, 'event) stream * 'event) list Hashtbl.M(Tnode).t;
+      (** The streams that most recently have been reading from a node's on-host array. The
+          completed events are removed opportunistically. *)
+  host_writing_streams :
+    (('buffer_ptr, 'dev, 'runner, 'event) stream * 'event) list Hashtbl.M(Tnode).t;
+      (** The streams that most recently have been writing to a node's on-host array. The completed
+          events are removed opportunistically. *)
 }
 [@@deriving sexp_of]
 
@@ -116,7 +122,11 @@ and ('buffer_ptr, 'dev, 'runner, 'event) stream = {
   stream_id : int;  (** An ID unique within the device. *)
   mutable allocated_buffer : 'buffer_ptr buffer option;
   updating_for : 'event Hashtbl.M(Tnode).t;
-      (* The completion event for updating (writing to) a node via this stream, if any. *)
+  (* The completion event for updating (writing to) a node via this stream, if any. *)
+  reader_streams : (('buffer_ptr, 'dev, 'runner, 'event) stream * 'event) list Hashtbl.M(Tnode).t;
+      (** The streams, other than this stream, that most recently have been reading from a node in
+          this stream's context, and the associated use completion events. The completed events are
+          removed opportunistically. *)
 }
 [@@deriving sexp_of]
 
@@ -214,8 +224,7 @@ module type Backend_device_common = sig
   (** Schedules waiting for the given event on the context's stream.
 
       NOTE: it should rarely be needed to call [will_wait_for] explicitly, because it is typically
-      called internally when necessary. But there is one exception, see {!device_to_device} when
-      [into_merge_buffer=Streaming]. *)
+      called internally when necessary. *)
 
   val get_used_memory : device -> int
   (** Returns (an upper bound of) the memory used for arrays, in bytes. *)
@@ -257,12 +266,15 @@ module type With_buffer_retrieval_and_syncing = sig
       - If the node is absent from the [src] context and either it is present in the [dst] context
         or [into_merge_buffer] is different from [No]: raises an error.
       - If the node is absent from [dst] and [into_merge_buffer=No]: returns false.
-      - Executes [will_wait_for dst (work_for src tn)].
-      - If [into_merge_buffer=No]: schedules a copy of the tensor node from [src] to [dst].
+      - Schedules waiting for writing into the tensor node on [src] to finish, if any.
+      - If [into_merge_buffer=No]: schedules a copy of the tensor node from [src] to [dst] and
+        updates the writer event for the node.
       - If [into_merge_buffer] is different from [No]: sets on [dst] the merge buffer source to the
-        given node. If [into_merge_buffer=Streaming], remembers the buffer pointer of the source
-        node to use for streaming, without blocking. If [into_merge_buffer=Copy], schedules copying
-        from [src] to the merge buffer of [dst]'s stream.
+        given node.
+      - If [into_merge_buffer=Streaming], remembers the buffer pointer of the source node to use for
+        streaming.
+      - If [into_merge_buffer=Copy], schedules copying from [src] to the merge buffer of [dst]'s
+        stream, and registers [dst.stream] with a reader event for the node.
 
       NOTE: If [into_merge_buffer=Streaming], after scheduling the work on [dst] using the merge
       buffer but before scheduling work on [src] that modifies [tn], execute
diff --git a/arrayjit/lib/backends.ml b/arrayjit/lib/backends.ml
index c699c85..27d5846 100644
--- a/arrayjit/lib/backends.ml
+++ b/arrayjit/lib/backends.ml
@@ -30,32 +30,42 @@ module Add_buffer_retrieval_and_syncing (Backend : No_buffer_retrieval_or_syncin
     |> List.iter ~f:(fun (work_stream, e) ->
            if not (equal_stream work_stream s) then Backend.will_wait_for ctx e)
 
-  let update_writer_event s tn =
+  let update_writer_event ?(from_host = false) s tn =
     let e = Backend.all_work s in
-    Hashtbl.update s.device.writer_streams tn ~f:(fun l -> (s, e) :: Option.value ~default:[] l);
+    if from_host then
+      Hashtbl.update s.device.host_writing_streams tn ~f:(fun l ->
+          (s, e) :: Option.value ~default:[] l);
+    (* To be on the safe side, record events for potentially cross-stream nodes. *)
+    if Tn.potentially_cross_stream tn then
+      Hashtbl.update s.device.shared_writer_streams tn ~f:(fun l ->
+          (s, e) :: Option.value ~default:[] l);
     Hashtbl.update s.updating_for tn ~f:(fun _ -> e)
 
-  let add_reader s tn =
+  let add_reader s tn from =
     let e = Backend.all_work s in
-    Hashtbl.update s.device.reader_streams tn ~f:(fun l -> (s, e) :: Option.value ~default:[] l)
+    let f l = (s, e) :: Option.value ~default:[] l in
+    match from with
+    | `Host -> Hashtbl.update s.device.host_reading_streams tn ~f
+    | `Src src -> Hashtbl.update src.reader_streams tn ~f
 
   let%diagn2_l_sexp from_host (ctx : Backend.context) tn =
     match (tn, Map.find ctx.ctx_arrays tn) with
     | { Tn.array = (lazy (Some hosted)); _ }, Some dst ->
-        wait_for_all ctx ctx.stream.device.reader_streams tn;
+        wait_for_all ctx ctx.stream.reader_streams tn;
         [%log "copying", Tn.debug_name tn, "to", (dst : Backend.buffer_ptr), "from host"];
         Backend.from_host ~dst_ptr:dst ~dst:ctx hosted;
-        update_writer_event ctx.stream tn;
+        update_writer_event ~from_host:true ctx.stream tn;
+        add_reader ctx.stream tn @@ `Host;
         true
     | _ -> false
 
   let%diagn2_l_sexp to_host (ctx : Backend.context) (tn : Tn.t) =
     match (tn, Map.find ctx.ctx_arrays tn) with
     | { Tn.array = (lazy (Some hosted)); _ }, Some src ->
-        wait_for_all ctx ctx.stream.device.writer_streams tn;
+        if Tn.potentially_cross_stream tn then
+          wait_for_all ctx ctx.stream.device.shared_writer_streams tn;
         [%log "copying", Tn.debug_name tn, "at", (src : Backend.buffer_ptr), "to host"];
         Backend.to_host ~src_ptr:src ~src:ctx hosted;
-        add_reader ctx.stream tn;
         true
     | _ -> false
 
@@ -343,13 +353,13 @@ module Raise_backend (Device : Lowered_backend) : Backend = struct
           let data = Hashtbl.find_or_add device.cross_stream_candidates key ~default in
           Map.add_exn ctx_arrays ~key ~data)
       else if Tn.known_shared_cross_stream key then (
-        if Hashtbl.mem device.owner_streams key then (
-          if not (equal_stream stream (Hashtbl.find_exn device.owner_streams key)) then
+        if Hashtbl.mem device.owner_stream key then (
+          if not (equal_stream stream (Hashtbl.find_exn device.owner_stream key)) then
             raise
             @@ Utils.User_error
                  ("Cuda_backend.alloc_if_needed: node " ^ Tn.debug_name key
                 ^ " assumed to be cross-stream-shared but then written to on multiple devices"))
-        else Hashtbl.add_exn device.owner_streams ~key ~data:stream;
+        else Hashtbl.add_exn device.owner_stream ~key ~data:stream;
         let data = Hashtbl.find_exn device.cross_stream_candidates key in
         Map.add_exn ctx_arrays ~key ~data)
       else (
diff --git a/arrayjit/lib/tnode.ml b/arrayjit/lib/tnode.ml
index 91afe01..5fb7e7c 100644
--- a/arrayjit/lib/tnode.ml
+++ b/arrayjit/lib/tnode.ml
@@ -247,6 +247,8 @@ let known_non_cross_stream tn =
   | Some ((On_device Per_stream | Hosted (Changed_on_devices Per_stream)), _) -> true
   | _ -> false
 
+let potentially_cross_stream tn = not (known_not_materialized tn || known_non_cross_stream tn)
+
 let mode_is_unspecified tn =
   match tn.memory_mode with
   | None | Some ((Never_virtual | Effectively_constant), _) -> true