diff --git a/synapse/storage/event_push_actions.py b/synapse/storage/event_push_actions.py
index 5f1b6f63a..3d93285f8 100644
--- a/synapse/storage/event_push_actions.py
+++ b/synapse/storage/event_push_actions.py
@@ -16,6 +16,8 @@
 from ._base import SQLBaseStore
 from twisted.internet import defer
 from synapse.util.caches.descriptors import cachedInlineCallbacks
+from synapse.types import RoomStreamToken
+from .stream import lower_bound
 
 import logging
 import ujson as json
@@ -73,6 +75,9 @@ class EventPushActionsStore(SQLBaseStore):
 
             stream_ordering = results[0][0]
             topological_ordering = results[0][1]
+            token = RoomStreamToken(
+                topological_ordering, stream_ordering
+            )
 
             sql = (
                 "SELECT sum(notif), sum(highlight)"
@@ -80,15 +85,10 @@ class EventPushActionsStore(SQLBaseStore):
                 " WHERE"
                 " user_id = ?"
                 " AND room_id = ?"
-                " AND ("
-                "       topological_ordering > ?"
-                "       OR (topological_ordering = ? AND stream_ordering > ?)"
-                ")"
-            )
-            txn.execute(sql, (
-                user_id, room_id,
-                topological_ordering, topological_ordering, stream_ordering
-            ))
+                " AND %s"
+            ) % (lower_bound(token, self.database_engine, inclusive=False),)
+
+            txn.execute(sql, (user_id, room_id))
             row = txn.fetchone()
             if row:
                 return {
diff --git a/synapse/storage/stream.py b/synapse/storage/stream.py
index b9ad965fd..c08c5b997 100644
--- a/synapse/storage/stream.py
+++ b/synapse/storage/stream.py
@@ -40,6 +40,7 @@ from synapse.util.caches.descriptors import cached
 from synapse.api.constants import EventTypes
 from synapse.types import RoomStreamToken
 from synapse.util.logcontext import preserve_fn
+from synapse.storage.engines import PostgresEngine, Sqlite3Engine
 
 import logging
 
@@ -54,25 +55,43 @@ _STREAM_TOKEN = "stream"
 _TOPOLOGICAL_TOKEN = "topological"
 
 
-def lower_bound(token):
+def lower_bound(token, engine, inclusive=False):
+    inclusive = "=" if inclusive else ""
     if token.topological is None:
-        return "(%d < %s)" % (token.stream, "stream_ordering")
+        return "(%d <%s %s)" % (token.stream, inclusive, "stream_ordering")
     else:
-        return "(%d < %s OR (%d = %s AND %d < %s))" % (
+        if isinstance(engine, PostgresEngine):
+            # Postgres doesn't optimise ``(x < a) OR (x=a AND y<b)`` as well
+            # as it optimises ``(x,y) < (a,b)`` on multicolumn indexes. So we
+            # use the later form when running against postgres.
+            return "((%d,%d) <%s (%s,%s))" % (
+                token.topological, token.stream, inclusive,
+                "topological_ordering", "stream_ordering",
+            )
+        return "(%d < %s OR (%d = %s AND %d <%s %s))" % (
             token.topological, "topological_ordering",
             token.topological, "topological_ordering",
-            token.stream, "stream_ordering",
+            token.stream, inclusive, "stream_ordering",
         )
 
 
-def upper_bound(token):
+def upper_bound(token, engine, inclusive=True):
+    inclusive = "=" if inclusive else ""
     if token.topological is None:
-        return "(%d >= %s)" % (token.stream, "stream_ordering")
+        return "(%d >%s %s)" % (token.stream, inclusive, "stream_ordering")
     else:
-        return "(%d > %s OR (%d = %s AND %d >= %s))" % (
+        if isinstance(engine, PostgresEngine):
+            # Postgres doesn't optimise ``(x > a) OR (x=a AND y>b)`` as well
+            # as it optimises ``(x,y) > (a,b)`` on multicolumn indexes. So we
+            # use the later form when running against postgres.
+            return "((%d,%d) >%s (%s,%s))" % (
+                token.topological, token.stream, inclusive,
+                "topological_ordering", "stream_ordering",
+            )
+        return "(%d > %s OR (%d = %s AND %d >%s %s))" % (
             token.topological, "topological_ordering",
             token.topological, "topological_ordering",
-            token.stream, "stream_ordering",
+            token.stream, inclusive, "stream_ordering",
         )
 
 
@@ -308,18 +327,22 @@ class StreamStore(SQLBaseStore):
         args = [False, room_id]
         if direction == 'b':
             order = "DESC"
-            bounds = upper_bound(RoomStreamToken.parse(from_key))
+            bounds = upper_bound(
+                RoomStreamToken.parse(from_key), self.database_engine
+            )
             if to_key:
-                bounds = "%s AND %s" % (
-                    bounds, lower_bound(RoomStreamToken.parse(to_key))
-                )
+                bounds = "%s AND %s" % (bounds, lower_bound(
+                    RoomStreamToken.parse(to_key), self.database_engine
+                ))
         else:
             order = "ASC"
-            bounds = lower_bound(RoomStreamToken.parse(from_key))
+            bounds = lower_bound(
+                RoomStreamToken.parse(from_key), self.database_engine
+            )
             if to_key:
-                bounds = "%s AND %s" % (
-                    bounds, upper_bound(RoomStreamToken.parse(to_key))
-                )
+                bounds = "%s AND %s" % (bounds, upper_bound(
+                    RoomStreamToken.parse(to_key), self.database_engine
+                ))
 
         if int(limit) > 0:
             args.append(int(limit))
@@ -586,32 +609,60 @@ class StreamStore(SQLBaseStore):
             retcols=["stream_ordering", "topological_ordering"],
         )
 
-        stream_ordering = results["stream_ordering"]
-        topological_ordering = results["topological_ordering"]
-
-        query_before = (
-            "SELECT topological_ordering, stream_ordering, event_id FROM events"
-            " WHERE room_id = ? AND (topological_ordering < ?"
-            " OR (topological_ordering = ? AND stream_ordering < ?))"
-            " ORDER BY topological_ordering DESC, stream_ordering DESC"
-            " LIMIT ?"
+        token = RoomStreamToken(
+            results["topological_ordering"],
+            results["stream_ordering"],
         )
 
-        query_after = (
-            "SELECT topological_ordering, stream_ordering, event_id FROM events"
-            " WHERE room_id = ? AND (topological_ordering > ?"
-            " OR (topological_ordering = ? AND stream_ordering > ?))"
-            " ORDER BY topological_ordering ASC, stream_ordering ASC"
-            " LIMIT ?"
-        )
+        if isinstance(self.database_engine, Sqlite3Engine):
+            # SQLite3 doesn't optimise ``(x < a) OR (x = a AND y < b)``
+            # So we give pass it to SQLite3 as the UNION ALL of the two queries.
 
-        txn.execute(
-            query_before,
-            (
-                room_id, topological_ordering, topological_ordering,
-                stream_ordering, before_limit,
+            query_before = (
+                "SELECT topological_ordering, stream_ordering, event_id FROM events"
+                " WHERE room_id = ? AND topological_ordering < ?"
+                " UNION ALL"
+                " SELECT topological_ordering, stream_ordering, event_id FROM events"
+                " WHERE room_id = ? AND topological_ordering = ? AND stream_ordering < ?"
+                " ORDER BY topological_ordering DESC, stream_ordering DESC LIMIT ?"
             )
-        )
+            before_args = (
+                room_id, token.topological,
+                room_id, token.topological, token.stream,
+                before_limit,
+            )
+
+            query_after = (
+                "SELECT topological_ordering, stream_ordering, event_id FROM events"
+                " WHERE room_id = ? AND topological_ordering > ?"
+                " UNION ALL"
+                " SELECT topological_ordering, stream_ordering, event_id FROM events"
+                " WHERE room_id = ? AND topological_ordering = ? AND stream_ordering > ?"
+                " ORDER BY topological_ordering ASC, stream_ordering ASC LIMIT ?"
+            )
+            after_args = (
+                room_id, token.topological,
+                room_id, token.topological, token.stream,
+                after_limit,
+            )
+        else:
+            query_before = (
+                "SELECT topological_ordering, stream_ordering, event_id FROM events"
+                " WHERE room_id = ? AND %s"
+                " ORDER BY topological_ordering DESC, stream_ordering DESC LIMIT ?"
+            ) % (upper_bound(token, self.database_engine, inclusive=False),)
+
+            before_args = (room_id, before_limit)
+
+            query_after = (
+                "SELECT topological_ordering, stream_ordering, event_id FROM events"
+                " WHERE room_id = ? AND %s"
+                " ORDER BY topological_ordering ASC, stream_ordering ASC LIMIT ?"
+            ) % (lower_bound(token, self.database_engine, inclusive=False),)
+
+            after_args = (room_id, after_limit)
+
+        txn.execute(query_before, before_args)
 
         rows = self.cursor_to_dict(txn)
         events_before = [r["event_id"] for r in rows]
@@ -623,17 +674,11 @@ class StreamStore(SQLBaseStore):
             ))
         else:
             start_token = str(RoomStreamToken(
-                topological_ordering,
-                stream_ordering - 1,
+                token.topological,
+                token.stream - 1,
             ))
 
-        txn.execute(
-            query_after,
-            (
-                room_id, topological_ordering, topological_ordering,
-                stream_ordering, after_limit,
-            )
-        )
+        txn.execute(query_after, after_args)
 
         rows = self.cursor_to_dict(txn)
         events_after = [r["event_id"] for r in rows]
@@ -644,10 +689,7 @@ class StreamStore(SQLBaseStore):
                 rows[-1]["stream_ordering"],
             ))
         else:
-            end_token = str(RoomStreamToken(
-                topological_ordering,
-                stream_ordering,
-            ))
+            end_token = str(token)
 
         return {
             "before": {