diff --git a/synapse/federation/send_queue.py b/synapse/federation/send_queue.py
index 945832283f..93e5acebc1 100644
--- a/synapse/federation/send_queue.py
+++ b/synapse/federation/send_queue.py
@@ -35,7 +35,7 @@ from synapse.storage.presence import UserPresenceState
 from synapse.util.metrics import Measure
 import synapse.metrics
 
-from sortedcontainers import SortedDict
+from blist import sorteddict
 from collections import namedtuple
 
 import logging
@@ -56,19 +56,19 @@ class FederationRemoteSendQueue(object):
         self.is_mine_id = hs.is_mine_id
 
         self.presence_map = {}  # Pending presence map user_id -> UserPresenceState
-        self.presence_changed = SortedDict()  # Stream position -> user_id
+        self.presence_changed = sorteddict()  # Stream position -> user_id
 
         self.keyed_edu = {}  # (destination, key) -> EDU
-        self.keyed_edu_changed = SortedDict()  # stream position -> (destination, key)
+        self.keyed_edu_changed = sorteddict()  # stream position -> (destination, key)
 
-        self.edus = SortedDict()  # stream position -> Edu
+        self.edus = sorteddict()  # stream position -> Edu
 
-        self.failures = SortedDict()  # stream position -> (destination, Failure)
+        self.failures = sorteddict()  # stream position -> (destination, Failure)
 
-        self.device_messages = SortedDict()  # stream position -> destination
+        self.device_messages = sorteddict()  # stream position -> destination
 
         self.pos = 1
-        self.pos_time = SortedDict()
+        self.pos_time = sorteddict()
 
         # EVERYTHING IS SAD. In particular, python only makes new scopes when
         # we make a new function, so we need to make a new function so the inner
diff --git a/synapse/python_dependencies.py b/synapse/python_dependencies.py
index f9596bddaf..40eedb63cb 100644
--- a/synapse/python_dependencies.py
+++ b/synapse/python_dependencies.py
@@ -34,8 +34,8 @@ REQUIREMENTS = {
     "bcrypt": ["bcrypt>=3.1.0"],
     "pillow": ["PIL"],
     "pydenticon": ["pydenticon"],
+    "blist": ["blist"],
     "pysaml2>=3.0.0": ["saml2>=3.0.0"],
-    "sortedcontainers": ["sortedcontainers"],
     "pymacaroons-pynacl": ["pymacaroons"],
     "msgpack-python>=0.3.0": ["msgpack"],
     "phonenumbers>=8.2.0": ["phonenumbers"],
diff --git a/synapse/util/caches/stream_change_cache.py b/synapse/util/caches/stream_change_cache.py
index 2ff46090a6..941d873ab8 100644
--- a/synapse/util/caches/stream_change_cache.py
+++ b/synapse/util/caches/stream_change_cache.py
@@ -16,7 +16,7 @@
 from synapse.util.caches import register_cache, CACHE_SIZE_FACTOR
 
 
-from sortedcontainers import SortedDict
+from blist import sorteddict
 import logging
 
 
@@ -35,7 +35,7 @@ class StreamChangeCache(object):
     def __init__(self, name, current_stream_pos, max_size=10000, prefilled_cache={}):
         self._max_size = int(max_size * CACHE_SIZE_FACTOR)
         self._entity_to_key = {}
-        self._cache = SortedDict()
+        self._cache = sorteddict()
         self._earliest_known_stream_pos = current_stream_pos
         self.name = name
         self.metrics = register_cache(self.name, self._cache)