diff --git a/poetry.lock b/poetry.lock
index 3a08c9478d..c535625cbf 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -57,6 +57,14 @@ six = ">=1.4.1"
 tests = ["pytest (>=3.2.1,!=3.3.0)"]
 typecheck = ["mypy"]
 
+[[package]]
+name = "bitarray"
+version = "2.5.1"
+description = "efficient arrays of booleans -- C extension"
+category = "main"
+optional = false
+python-versions = "*"
+
 [[package]]
 name = "black"
 version = "22.3.0"
@@ -562,6 +570,14 @@ category = "dev"
 optional = false
 python-versions = "*"
 
+[[package]]
+name = "mmh3"
+version = "3.0.0"
+description = "Python wrapper for MurmurHash (MurmurHash3), a set of fast and robust hash functions."
+category = "main"
+optional = false
+python-versions = "*"
+
 [[package]]
 name = "msgpack"
 version = "1.0.3"
@@ -1007,6 +1023,18 @@ python-versions = ">=3.7"
 [package.extras]
 idna2008 = ["idna"]
 
+[[package]]
+name = "scalable-cuckoo-filter"
+version = "1.1"
+description = "Scalable Cuckoo filter"
+category = "main"
+optional = false
+python-versions = "*"
+
+[package.dependencies]
+bitarray = "*"
+mmh3 = "*"
+
 [[package]]
 name = "secretstorage"
 version = "3.3.1"
@@ -1563,7 +1591,7 @@ url_preview = ["lxml"]
 [metadata]
 lock-version = "1.1"
 python-versions = "^3.7.1"
-content-hash = "e96625923122e29b6ea5964379828e321b6cede2b020fc32c6f86c09d86d1ae8"
+content-hash = "2cef6331212eb5346293254c8bf2c14f967ce240cea24f87cff7a21ced3160da"
 
 [metadata.files]
 attrs = [
@@ -1590,6 +1618,7 @@ bcrypt = [
     {file = "bcrypt-3.2.0-cp36-abi3-win_amd64.whl", hash = "sha256:81fec756feff5b6818ea7ab031205e1d323d8943d237303baca2c5f9c7846f34"},
     {file = "bcrypt-3.2.0.tar.gz", hash = "sha256:5b93c1726e50a93a033c36e5ca7fdcd29a5c7395af50a6892f5d9e7c6cfbfb29"},
 ]
+bitarray = []
 black = [
     {file = "black-22.3.0-cp310-cp310-macosx_10_9_universal2.whl", hash = "sha256:2497f9c2386572e28921fa8bec7be3e51de6801f7459dffd6e62492531c47e09"},
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@@ -1936,78 +1965,7 @@ ldap3 = [
     {file = "ldap3-2.9.1-py3.9.egg", hash = "sha256:5630d1383e09ba94839e253e013f1aa1a2cf7a547628ba1265cb7b9a844b5687"},
     {file = "ldap3-2.9.1.tar.gz", hash = "sha256:f3e7fc4718e3f09dda568b57100095e0ce58633bcabbed8667ce3f8fbaa4229f"},
 ]
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 mccabe = [
     {file = "mccabe-0.6.1-py2.py3-none-any.whl", hash = "sha256:ab8a6258860da4b6677da4bd2fe5dc2c659cff31b3ee4f7f5d64e79735b80d42"},
     {file = "mccabe-0.6.1.tar.gz", hash = "sha256:dd8d182285a0fe56bace7f45b5e7d1a6ebcbf524e8f3bd87eb0f125271b8831f"},
 ]
+mmh3 = []
 msgpack = [
     {file = "msgpack-1.0.3-cp310-cp310-macosx_10_9_universal2.whl", hash = "sha256:96acc674bb9c9be63fa8b6dabc3248fdc575c4adc005c440ad02f87ca7edd079"},
     {file = "msgpack-1.0.3-cp310-cp310-macosx_10_9_x86_64.whl", hash = "sha256:2c3ca57c96c8e69c1a0d2926a6acf2d9a522b41dc4253a8945c4c6cd4981a4e3"},
@@ -2394,6 +2350,7 @@ rfc3986 = [
     {file = "rfc3986-2.0.0-py2.py3-none-any.whl", hash = "sha256:50b1502b60e289cb37883f3dfd34532b8873c7de9f49bb546641ce9cbd256ebd"},
     {file = "rfc3986-2.0.0.tar.gz", hash = "sha256:97aacf9dbd4bfd829baad6e6309fa6573aaf1be3f6fa735c8ab05e46cecb261c"},
 ]
+scalable-cuckoo-filter = []
 secretstorage = [
     {file = "SecretStorage-3.3.1-py3-none-any.whl", hash = "sha256:422d82c36172d88d6a0ed5afdec956514b189ddbfb72fefab0c8a1cee4eaf71f"},
     {file = "SecretStorage-3.3.1.tar.gz", hash = "sha256:fd666c51a6bf200643495a04abb261f83229dcb6fd8472ec393df7ffc8b6f195"},
diff --git a/pyproject.toml b/pyproject.toml
index f77c02ca27..5575c56de1 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -180,6 +180,7 @@ hiredis = { version = "*", optional = true }
 Pympler = { version = "*", optional = true }
 parameterized = { version = ">=0.7.4", optional = true }
 idna = { version = ">=2.5", optional = true }
+scalable-cuckoo-filter = "^1.1"
 
 [tool.poetry.extras]
 # NB: Packages that should be part of `pip install matrix-synapse[all]` need to be specified
diff --git a/synapse/util/caches/lrucache.py b/synapse/util/caches/lrucache.py
index 31f41fec82..c640c238d5 100644
--- a/synapse/util/caches/lrucache.py
+++ b/synapse/util/caches/lrucache.py
@@ -34,6 +34,7 @@ from typing import (
     overload,
 )
 
+from cuckoo.filter import ScalableCuckooFilter
 from typing_extensions import Literal
 
 from twisted.internet import reactor
@@ -427,6 +428,17 @@ class LruCache(Generic[KT, VT]):
         else:
             self.max_size = int(max_size)
 
+        self._doorkeeper = ScalableCuckooFilter(
+            initial_capacity=self.max_size, error_rate=0.001
+        )
+        self._doorkeeper_2 = ScalableCuckooFilter(self.max_size, 0.001)
+
+        def _rotate_doorkeeper() -> None:
+            self._doorkeeper_2 = self._doorkeeper
+            self._doorkeeper = ScalableCuckooFilter(self.max_size, 0.001)
+
+        real_clock.looping_call(_rotate_doorkeeper, 5 * 60 * 100)
+
         # register_cache might call our "set_cache_factor" callback; there's nothing to
         # do yet when we get resized.
         self._on_resize: Optional[Callable[[], None]] = None
@@ -496,6 +508,14 @@ class LruCache(Generic[KT, VT]):
         def add_node(
             key: KT, value: VT, callbacks: Collection[Callable[[], None]] = ()
         ) -> None:
+            hash_key = hash(()).to_bytes(8, byteorder="big")
+            found = self._doorkeeper.contains(hash_key) | self._doorkeeper_2.contains(
+                hash_key
+            )
+            if not found:
+                self._doorkeeper.insert(hash_key)
+                return
+
             node: _Node[KT, VT] = _Node(
                 list_root,
                 key,