diff --git a/synapse/federation/send_queue.py b/synapse/federation/send_queue.py
index 0f4aea95a3..1d5c0f3797 100644
--- a/synapse/federation/send_queue.py
+++ b/synapse/federation/send_queue.py
@@ -98,7 +98,7 @@ class FederationRemoteSendQueue(object):
         now = self.clock.time_msec()
 
         keys = self.pos_time.keys()
-        time = keys.bisect_left(now - FIVE_MINUTES_AGO)
+        time = self.pos_time.bisect_left(now - FIVE_MINUTES_AGO)
         if not keys[:time]:
             return
 
@@ -113,7 +113,7 @@ class FederationRemoteSendQueue(object):
         with Measure(self.clock, "send_queue._clear"):
             # Delete things out of presence maps
             keys = self.presence_changed.keys()
-            i = keys.bisect_left(position_to_delete)
+            i = self.presence_changed.bisect_left(position_to_delete)
             for key in keys[:i]:
                 del self.presence_changed[key]
 
@@ -131,7 +131,7 @@ class FederationRemoteSendQueue(object):
 
             # Delete things out of keyed edus
             keys = self.keyed_edu_changed.keys()
-            i = keys.bisect_left(position_to_delete)
+            i = self.keyed_edu_changed.bisect_left(position_to_delete)
             for key in keys[:i]:
                 del self.keyed_edu_changed[key]
 
@@ -145,19 +145,19 @@ class FederationRemoteSendQueue(object):
 
             # Delete things out of edu map
             keys = self.edus.keys()
-            i = keys.bisect_left(position_to_delete)
+            i = self.edus.bisect_left(position_to_delete)
             for key in keys[:i]:
                 del self.edus[key]
 
             # Delete things out of failure map
             keys = self.failures.keys()
-            i = keys.bisect_left(position_to_delete)
+            i = self.failures.bisect_left(position_to_delete)
             for key in keys[:i]:
                 del self.failures[key]
 
             # Delete things out of device map
             keys = self.device_messages.keys()
-            i = keys.bisect_left(position_to_delete)
+            i = self.device_messages.bisect_left(position_to_delete)
             for key in keys[:i]:
                 del self.device_messages[key]
 
@@ -250,13 +250,12 @@ class FederationRemoteSendQueue(object):
             self._clear_queue_before_pos(federation_ack)
 
         # Fetch changed presence
-        keys = self.presence_changed.keys()
-        i = keys.bisect_right(from_token)
-        j = keys.bisect_right(to_token) + 1
+        i = self.presence_changed.bisect_right(from_token)
+        j = self.presence_changed.bisect_right(to_token) + 1
         dest_user_ids = [
             (pos, user_id)
-            for pos in keys[i:j]
-            for user_id in self.presence_changed[pos]
+            for pos, user_id_list in self.presence_changed.items()[i:j]
+            for user_id in user_id_list
         ]
 
         for (key, user_id) in dest_user_ids:
@@ -265,13 +264,12 @@ class FederationRemoteSendQueue(object):
             )))
 
         # Fetch changes keyed edus
-        keys = self.keyed_edu_changed.keys()
-        i = keys.bisect_right(from_token)
-        j = keys.bisect_right(to_token) + 1
+        i = self.keyed_edu_changed.bisect_right(from_token)
+        j = self.keyed_edu_changed.bisect_right(to_token) + 1
         # We purposefully clobber based on the key here, python dict comprehensions
         # always use the last value, so this will correctly point to the last
         # stream position.
-        keyed_edus = {self.keyed_edu_changed[k]: k for k in keys[i:j]}
+        keyed_edus = {v: k for k, v in self.keyed_edu_changed.items()[i:j]}
 
         for ((destination, edu_key), pos) in iteritems(keyed_edus):
             rows.append((pos, KeyedEduRow(
@@ -280,19 +278,17 @@ class FederationRemoteSendQueue(object):
             )))
 
         # Fetch changed edus
-        keys = self.edus.keys()
-        i = keys.bisect_right(from_token)
-        j = keys.bisect_right(to_token) + 1
-        edus = ((k, self.edus[k]) for k in keys[i:j])
+        i = self.edus.bisect_right(from_token)
+        j = self.edus.bisect_right(to_token) + 1
+        edus = self.edus.items()[i:j]
 
         for (pos, edu) in edus:
             rows.append((pos, EduRow(edu)))
 
         # Fetch changed failures
-        keys = self.failures.keys()
-        i = keys.bisect_right(from_token)
-        j = keys.bisect_right(to_token) + 1
-        failures = ((k, self.failures[k]) for k in keys[i:j])
+        i = self.failures.bisect_right(from_token)
+        j = self.failures.bisect_right(to_token) + 1
+        failures = self.failures.items()[i:j]
 
         for (pos, (destination, failure)) in failures:
             rows.append((pos, FailureRow(
@@ -301,10 +297,9 @@ class FederationRemoteSendQueue(object):
             )))
 
         # Fetch changed device messages
-        keys = self.device_messages.keys()
-        i = keys.bisect_right(from_token)
-        j = keys.bisect_right(to_token) + 1
-        device_messages = {self.device_messages[k]: k for k in keys[i:j]}
+        i = self.device_messages.bisect_right(from_token)
+        j = self.device_messages.bisect_right(to_token) + 1
+        device_messages = {v: k for k, v in self.device_messages.items()[i:j]}
 
         for (destination, pos) in iteritems(device_messages):
             rows.append((pos, DeviceRow(