diff --git a/synapse/handlers/room_member.py b/synapse/handlers/room_member.py
index 3ba5335af..ba49075a2 100644
--- a/synapse/handlers/room_member.py
+++ b/synapse/handlers/room_member.py
@@ -85,6 +85,12 @@ class RoomMemberHandler(BaseHandler):
             prev_event_ids=prev_event_ids,
         )
 
+        # Check if this event matches the previous membership event for the user.
+        duplicate = yield msg_handler.deduplicate_state_event(event, context)
+        if duplicate is not None:
+            # Discard the new event since this membership change is a no-op.
+            return
+
         yield msg_handler.handle_new_client_event(
             requester,
             event,
diff --git a/synapse/handlers/sync.py b/synapse/handlers/sync.py
index 14f2032af..b5962f4f5 100644
--- a/synapse/handlers/sync.py
+++ b/synapse/handlers/sync.py
@@ -576,7 +576,7 @@ class SyncHandler(object):
 
             logger.debug("Getting messages up to %d", now_token.to_device_key)
             messages, stream_id = yield self.store.get_new_messages_for_device(
-                user_id, device_id, now_token.to_device_key
+                user_id, device_id, since_stream_id, now_token.to_device_key
             )
             logger.debug("Got messages up to %d: %r", stream_id, messages)
             sync_result_builder.now_token = now_token.copy_and_replace(
diff --git a/synapse/storage/deviceinbox.py b/synapse/storage/deviceinbox.py
index 2fa0a218b..68116b039 100644
--- a/synapse/storage/deviceinbox.py
+++ b/synapse/storage/deviceinbox.py
@@ -85,7 +85,7 @@ class DeviceInboxStore(SQLBaseStore):
         defer.returnValue(self._device_inbox_id_gen.get_current_token())
 
     def get_new_messages_for_device(
-        self, user_id, device_id, current_stream_id, limit=100
+        self, user_id, device_id, last_stream_id, current_stream_id, limit=100
     ):
         """
         Args:
@@ -101,11 +101,13 @@ class DeviceInboxStore(SQLBaseStore):
             sql = (
                 "SELECT stream_id, message_json FROM device_inbox"
                 " WHERE user_id = ? AND device_id = ?"
-                " AND stream_id <= ?"
+                " AND ? < stream_id AND stream_id <= ?"
                 " ORDER BY stream_id ASC"
                 " LIMIT ?"
             )
-            txn.execute(sql, (user_id, device_id, current_stream_id, limit))
+            txn.execute(sql, (
+                user_id, device_id, last_stream_id, current_stream_id, limit
+            ))
             messages = []
             for row in txn.fetchall():
                 stream_pos = row[0]