diff --git a/changelog.d/6135.bugfix b/changelog.d/6135.bugfix
new file mode 100644
index 000000000..5f9f010cb
--- /dev/null
+++ b/changelog.d/6135.bugfix
@@ -0,0 +1 @@
+Fix bug in background update that adds last seen information to the `devices` table, and improve its performance on Postgres.
diff --git a/synapse/storage/client_ips.py b/synapse/storage/client_ips.py
index 539584288..bb135166c 100644
--- a/synapse/storage/client_ips.py
+++ b/synapse/storage/client_ips.py
@@ -463,14 +463,46 @@ class ClientIpStore(background_updates.BackgroundUpdateStore):
         last_device_id = progress.get("last_device_id", "")
 
         def _devices_last_seen_update_txn(txn):
+            # This consists of two queries:
+            #
+            #   1. The sub-query searches for the next N devices and joins
+            #      against user_ips to find the max last_seen associated with
+            #      that device.
+            #   2. The outer query then joins again against user_ips on
+            #      user/device/last_seen. This *should* hopefully only
+            #      return one row, but if it does return more than one then
+            #      we'll just end up updating the same device row multiple
+            #      times, which is fine.
+
+            if self.database_engine.supports_tuple_comparison:
+                where_clause = "(user_id, device_id) > (?, ?)"
+                where_args = [last_user_id, last_device_id]
+            else:
+                # We explicitly do a `user_id >= ? AND (...)` here to ensure
+                # that an index is used, as doing `user_id > ? OR (user_id = ? AND ...)`
+                # makes it hard for query optimiser to tell that it can use the
+                # index on user_id
+                where_clause = "user_id >= ? AND (user_id > ? OR device_id > ?)"
+                where_args = [last_user_id, last_user_id, last_device_id]
+
             sql = """
-                SELECT u.last_seen, u.ip, u.user_agent, user_id, device_id FROM devices
-                INNER JOIN user_ips AS u USING (user_id, device_id)
-                WHERE user_id > ? OR (user_id = ? AND device_id > ?)
-                ORDER BY user_id ASC, device_id ASC
-                LIMIT ?
-            """
-            txn.execute(sql, (last_user_id, last_user_id, last_device_id, batch_size))
+                SELECT
+                    last_seen, ip, user_agent, user_id, device_id
+                FROM (
+                    SELECT
+                        user_id, device_id, MAX(u.last_seen) AS last_seen
+                    FROM devices
+                    INNER JOIN user_ips AS u USING (user_id, device_id)
+                    WHERE %(where_clause)s
+                    GROUP BY user_id, device_id
+                    ORDER BY user_id ASC, device_id ASC
+                    LIMIT ?
+                ) c
+                INNER JOIN user_ips AS u USING (user_id, device_id, last_seen)
+            """ % {
+                "where_clause": where_clause
+            }
+            txn.execute(sql, where_args + [batch_size])
 
             rows = txn.fetchall()
             if not rows:
diff --git a/synapse/storage/engines/postgres.py b/synapse/storage/engines/postgres.py
index 289b6bc28..601617b21 100644
--- a/synapse/storage/engines/postgres.py
+++ b/synapse/storage/engines/postgres.py
@@ -72,6 +72,13 @@ class PostgresEngine(object):
         """
         return True
 
+    @property
+    def supports_tuple_comparison(self):
+        """
+        Do we support comparing tuples, i.e. `(a, b) > (c, d)`?
+        """
+        return True
+
     def is_deadlock(self, error):
         if isinstance(error, self.module.DatabaseError):
             # https://www.postgresql.org/docs/current/static/errcodes-appendix.html
diff --git a/synapse/storage/engines/sqlite.py b/synapse/storage/engines/sqlite.py
index e9b9caa49..ac9210936 100644
--- a/synapse/storage/engines/sqlite.py
+++ b/synapse/storage/engines/sqlite.py
@@ -38,6 +38,14 @@ class Sqlite3Engine(object):
         """
         return self.module.sqlite_version_info >= (3, 24, 0)
 
+    @property
+    def supports_tuple_comparison(self):
+        """
+        Do we support comparing tuples, i.e. `(a, b) > (c, d)`? This requires
+        SQLite 3.15+.
+        """
+        return self.module.sqlite_version_info >= (3, 15, 0)
+
     def check_database(self, txn):
         pass