diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index 96750cb6c8..7dbd83908e 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -280,7 +280,6 @@ jobs:
       - check-lockfile
       - lint-clippy
       - lint-rustfmt
-      - check-signoff
     runs-on: ubuntu-latest
     steps:
       - run: "true"
diff --git a/CHANGES.md b/CHANGES.md
index 6c30c40858..0ee3970e2b 100644
--- a/CHANGES.md
+++ b/CHANGES.md
@@ -1,3 +1,21 @@
+# Synapse 1.94.0 (2023-10-10)
+
+No significant changes since 1.94.0rc1.
+However, please take note of the security advisory that follows.
+
+## Security advisory
+
+The following issue is fixed in 1.94.0 (and RC).
+
+- [GHSA-5chr-wjw5-3gq4](https://github.com/matrix-org/synapse/security/advisories/GHSA-5chr-wjw5-3gq4) — Moderate Severity
+
+  A malicious server ACL event can impact performance temporarily or permanently leading to a persistent denial of service.
+
+  Homeservers running on a closed federation (which presumably do not need to use server ACLs) are not affected.
+
+See the advisory for more details. If you have any questions, email security@matrix.org.
+
+
 # Synapse 1.94.0rc1 (2023-10-03)
 
 ### Features
diff --git a/changelog.d/16454.misc b/changelog.d/16454.misc
new file mode 100644
index 0000000000..1e75dc436f
--- /dev/null
+++ b/changelog.d/16454.misc
@@ -0,0 +1 @@
+Do not block running of CI behind the check for sign-off on PRs.
diff --git a/changelog.d/16455.bugfix b/changelog.d/16455.bugfix
new file mode 100644
index 0000000000..653a25d3b6
--- /dev/null
+++ b/changelog.d/16455.bugfix
@@ -0,0 +1 @@
+Prevent the purging of large rooms from timing out when Postgres is in use. The timeout which causes this issue was introduced in Synapse 1.88.0.
diff --git a/changelog.d/16457.bugfix b/changelog.d/16457.bugfix
new file mode 100644
index 0000000000..b9a95cc510
--- /dev/null
+++ b/changelog.d/16457.bugfix
@@ -0,0 +1 @@
+Improve the performance of purging rooms, particularly encrypted rooms.
diff --git a/debian/changelog b/debian/changelog
index 78da69ebb0..57479ca8e5 100644
--- a/debian/changelog
+++ b/debian/changelog
@@ -1,3 +1,9 @@
+matrix-synapse-py3 (1.94.0) stable; urgency=medium
+
+  * New Synapse release 1.94.0.
+
+ -- Synapse Packaging team <packages@matrix.org>  Tue, 10 Oct 2023 10:57:41 +0100
+
 matrix-synapse-py3 (1.94.0~rc1) stable; urgency=medium
 
   * New Synapse release 1.94.0rc1.
diff --git a/poetry.lock b/poetry.lock
index 13884e6698..a1a2b83764 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -208,13 +208,13 @@ uvloop = ["uvloop (>=0.15.2)"]
 
 [[package]]
 name = "bleach"
-version = "6.0.0"
+version = "6.1.0"
 description = "An easy safelist-based HTML-sanitizing tool."
 optional = false
-python-versions = ">=3.7"
+python-versions = ">=3.8"
 files = [
-    {file = "bleach-6.0.0-py3-none-any.whl", hash = "sha256:33c16e3353dbd13028ab4799a0f89a83f113405c766e9c122df8a06f5b85b3f4"},
-    {file = "bleach-6.0.0.tar.gz", hash = "sha256:1a1a85c1595e07d8db14c5f09f09e6433502c51c595970edc090551f0db99414"},
+    {file = "bleach-6.1.0-py3-none-any.whl", hash = "sha256:3225f354cfc436b9789c66c4ee030194bee0568fbf9cbdad3bc8b5c26c5f12b6"},
+    {file = "bleach-6.1.0.tar.gz", hash = "sha256:0a31f1837963c41d46bbf1331b8778e1308ea0791db03cc4e7357b97cf42a8fe"},
 ]
 
 [package.dependencies]
@@ -222,7 +222,7 @@ six = ">=1.9.0"
 webencodings = "*"
 
 [package.extras]
-css = ["tinycss2 (>=1.1.0,<1.2)"]
+css = ["tinycss2 (>=1.1.0,<1.3)"]
 
 [[package]]
 name = "canonicaljson"
@@ -1557,13 +1557,13 @@ testing-docutils = ["pygments", "pytest (>=7,<8)", "pytest-param-files (>=0.3.4,
 
 [[package]]
 name = "netaddr"
-version = "0.8.0"
+version = "0.9.0"
 description = "A network address manipulation library for Python"
 optional = false
 python-versions = "*"
 files = [
-    {file = "netaddr-0.8.0-py2.py3-none-any.whl", hash = "sha256:9666d0232c32d2656e5e5f8d735f58fd6c7457ce52fc21c98d45f2af78f990ac"},
-    {file = "netaddr-0.8.0.tar.gz", hash = "sha256:d6cc57c7a07b1d9d2e917aa8b36ae8ce61c35ba3fcd1b83ca31c5a0ee2b5a243"},
+    {file = "netaddr-0.9.0-py3-none-any.whl", hash = "sha256:5148b1055679d2a1ec070c521b7db82137887fabd6d7e37f5199b44f775c3bb1"},
+    {file = "netaddr-0.9.0.tar.gz", hash = "sha256:7b46fa9b1a2d71fd5de9e4a3784ef339700a53a08c8040f08baf5f1194da0128"},
 ]
 
 [[package]]
@@ -1749,22 +1749,22 @@ twisted = ["twisted"]
 
 [[package]]
 name = "psycopg2"
-version = "2.9.8"
+version = "2.9.9"
 description = "psycopg2 - Python-PostgreSQL Database Adapter"
 optional = true
-python-versions = ">=3.6"
+python-versions = ">=3.7"
 files = [
-    {file = "psycopg2-2.9.8-cp310-cp310-win32.whl", hash = "sha256:2f8594f92bbb5d8b59ffec04e2686c416401e2d4297de1193f8e75235937e71d"},
-    {file = "psycopg2-2.9.8-cp310-cp310-win_amd64.whl", hash = "sha256:f9ecbf504c4eaff90139d5c9b95d47275f2b2651e14eba56392b4041fbf4c2b3"},
-    {file = "psycopg2-2.9.8-cp311-cp311-win32.whl", hash = "sha256:65f81e72136d8b9ac8abf5206938d60f50da424149a43b6073f1546063c0565e"},
-    {file = "psycopg2-2.9.8-cp311-cp311-win_amd64.whl", hash = "sha256:f7e62095d749359b7854143843f27edd7dccfcd3e1d833b880562aa5702d92b0"},
-    {file = "psycopg2-2.9.8-cp37-cp37m-win32.whl", hash = "sha256:81b21424023a290a40884c7f8b0093ba6465b59bd785c18f757e76945f65594c"},
-    {file = "psycopg2-2.9.8-cp37-cp37m-win_amd64.whl", hash = "sha256:67c2f32f3aba79afb15799575e77ee2db6b46b8acf943c21d34d02d4e1041d50"},
-    {file = "psycopg2-2.9.8-cp38-cp38-win32.whl", hash = "sha256:287a64ef168ef7fb9f382964705ff664b342bfff47e7242bf0a04ef203269dd5"},
-    {file = "psycopg2-2.9.8-cp38-cp38-win_amd64.whl", hash = "sha256:dcde3cad4920e29e74bf4e76c072649764914facb2069e6b7fa1ddbebcd49e9f"},
-    {file = "psycopg2-2.9.8-cp39-cp39-win32.whl", hash = "sha256:d4ad050ea50a16731d219c3a85e8f2debf49415a070f0b8331ccc96c81700d9b"},
-    {file = "psycopg2-2.9.8-cp39-cp39-win_amd64.whl", hash = "sha256:d39bb3959788b2c9d7bf5ff762e29f436172b241cd7b47529baac77746fd7918"},
-    {file = "psycopg2-2.9.8.tar.gz", hash = "sha256:3da6488042a53b50933244085f3f91803f1b7271f970f3e5536efa69314f6a49"},
+    {file = "psycopg2-2.9.9-cp310-cp310-win32.whl", hash = "sha256:38a8dcc6856f569068b47de286b472b7c473ac7977243593a288ebce0dc89516"},
+    {file = "psycopg2-2.9.9-cp310-cp310-win_amd64.whl", hash = "sha256:426f9f29bde126913a20a96ff8ce7d73fd8a216cfb323b1f04da402d452853c3"},
+    {file = "psycopg2-2.9.9-cp311-cp311-win32.whl", hash = "sha256:ade01303ccf7ae12c356a5e10911c9e1c51136003a9a1d92f7aa9d010fb98372"},
+    {file = "psycopg2-2.9.9-cp311-cp311-win_amd64.whl", hash = "sha256:121081ea2e76729acfb0673ff33755e8703d45e926e416cb59bae3a86c6a4981"},
+    {file = "psycopg2-2.9.9-cp37-cp37m-win32.whl", hash = "sha256:5e0d98cade4f0e0304d7d6f25bbfbc5bd186e07b38eac65379309c4ca3193efa"},
+    {file = "psycopg2-2.9.9-cp37-cp37m-win_amd64.whl", hash = "sha256:7e2dacf8b009a1c1e843b5213a87f7c544b2b042476ed7755be813eaf4e8347a"},
+    {file = "psycopg2-2.9.9-cp38-cp38-win32.whl", hash = "sha256:ff432630e510709564c01dafdbe996cb552e0b9f3f065eb89bdce5bd31fabf4c"},
+    {file = "psycopg2-2.9.9-cp38-cp38-win_amd64.whl", hash = "sha256:bac58c024c9922c23550af2a581998624d6e02350f4ae9c5f0bc642c633a2d5e"},
+    {file = "psycopg2-2.9.9-cp39-cp39-win32.whl", hash = "sha256:c92811b2d4c9b6ea0285942b2e7cac98a59e166d59c588fe5cfe1eda58e72d59"},
+    {file = "psycopg2-2.9.9-cp39-cp39-win_amd64.whl", hash = "sha256:de80739447af31525feddeb8effd640782cf5998e1a4e9192ebdf829717e3913"},
+    {file = "psycopg2-2.9.9.tar.gz", hash = "sha256:d1454bde93fb1e224166811694d600e746430c006fbb031ea06ecc2ea41bf156"},
 ]
 
 [[package]]
@@ -2427,28 +2427,28 @@ files = [
 
 [[package]]
 name = "ruff"
-version = "0.0.290"
+version = "0.0.292"
 description = "An extremely fast Python linter, written in Rust."
 optional = false
 python-versions = ">=3.7"
 files = [
-    {file = "ruff-0.0.290-py3-none-macosx_10_7_x86_64.whl", hash = "sha256:0e2b09ac4213b11a3520221083866a5816616f3ae9da123037b8ab275066fbac"},
-    {file = "ruff-0.0.290-py3-none-macosx_10_9_x86_64.macosx_11_0_arm64.macosx_10_9_universal2.whl", hash = "sha256:4ca6285aa77b3d966be32c9a3cd531655b3d4a0171e1f9bf26d66d0372186767"},
-    {file = "ruff-0.0.290-py3-none-manylinux_2_17_aarch64.manylinux2014_aarch64.whl", hash = "sha256:35e3550d1d9f2157b0fcc77670f7bb59154f223bff281766e61bdd1dd854e0c5"},
-    {file = "ruff-0.0.290-py3-none-manylinux_2_17_armv7l.manylinux2014_armv7l.whl", hash = "sha256:d748c8bd97874f5751aed73e8dde379ce32d16338123d07c18b25c9a2796574a"},
-    {file = "ruff-0.0.290-py3-none-manylinux_2_17_i686.manylinux2014_i686.whl", hash = "sha256:982af5ec67cecd099e2ef5e238650407fb40d56304910102d054c109f390bf3c"},
-    {file = "ruff-0.0.290-py3-none-manylinux_2_17_ppc64.manylinux2014_ppc64.whl", hash = "sha256:bbd37352cea4ee007c48a44c9bc45a21f7ba70a57edfe46842e346651e2b995a"},
-    {file = "ruff-0.0.290-py3-none-manylinux_2_17_ppc64le.manylinux2014_ppc64le.whl", hash = "sha256:1d9be6351b7889462912e0b8185a260c0219c35dfd920fb490c7f256f1d8313e"},
-    {file = "ruff-0.0.290-py3-none-manylinux_2_17_s390x.manylinux2014_s390x.whl", hash = "sha256:75cdc7fe32dcf33b7cec306707552dda54632ac29402775b9e212a3c16aad5e6"},
-    {file = "ruff-0.0.290-py3-none-manylinux_2_17_x86_64.manylinux2014_x86_64.whl", hash = "sha256:eb07f37f7aecdbbc91d759c0c09870ce0fb3eed4025eebedf9c4b98c69abd527"},
-    {file = "ruff-0.0.290-py3-none-musllinux_1_2_aarch64.whl", hash = "sha256:2ab41bc0ba359d3f715fc7b705bdeef19c0461351306b70a4e247f836b9350ed"},
-    {file = "ruff-0.0.290-py3-none-musllinux_1_2_armv7l.whl", hash = "sha256:150bf8050214cea5b990945b66433bf9a5e0cef395c9bc0f50569e7de7540c86"},
-    {file = "ruff-0.0.290-py3-none-musllinux_1_2_i686.whl", hash = "sha256:75386ebc15fe5467248c039f5bf6a0cfe7bfc619ffbb8cd62406cd8811815fca"},
-    {file = "ruff-0.0.290-py3-none-musllinux_1_2_x86_64.whl", hash = "sha256:ac93eadf07bc4ab4c48d8bb4e427bf0f58f3a9c578862eb85d99d704669f5da0"},
-    {file = "ruff-0.0.290-py3-none-win32.whl", hash = "sha256:461fbd1fb9ca806d4e3d5c745a30e185f7cf3ca77293cdc17abb2f2a990ad3f7"},
-    {file = "ruff-0.0.290-py3-none-win_amd64.whl", hash = "sha256:f1f49f5ec967fd5778813780b12a5650ab0ebcb9ddcca28d642c689b36920796"},
-    {file = "ruff-0.0.290-py3-none-win_arm64.whl", hash = "sha256:ae5a92dfbdf1f0c689433c223f8dac0782c2b2584bd502dfdbc76475669f1ba1"},
-    {file = "ruff-0.0.290.tar.gz", hash = "sha256:949fecbc5467bb11b8db810a7fa53c7e02633856ee6bd1302b2f43adcd71b88d"},
+    {file = "ruff-0.0.292-py3-none-macosx_10_7_x86_64.whl", hash = "sha256:02f29db018c9d474270c704e6c6b13b18ed0ecac82761e4fcf0faa3728430c96"},
+    {file = "ruff-0.0.292-py3-none-macosx_10_9_x86_64.macosx_11_0_arm64.macosx_10_9_universal2.whl", hash = "sha256:69654e564342f507edfa09ee6897883ca76e331d4bbc3676d8a8403838e9fade"},
+    {file = "ruff-0.0.292-py3-none-manylinux_2_17_aarch64.manylinux2014_aarch64.whl", hash = "sha256:6c3c91859a9b845c33778f11902e7b26440d64b9d5110edd4e4fa1726c41e0a4"},
+    {file = "ruff-0.0.292-py3-none-manylinux_2_17_armv7l.manylinux2014_armv7l.whl", hash = "sha256:f4476f1243af2d8c29da5f235c13dca52177117935e1f9393f9d90f9833f69e4"},
+    {file = "ruff-0.0.292-py3-none-manylinux_2_17_i686.manylinux2014_i686.whl", hash = "sha256:be8eb50eaf8648070b8e58ece8e69c9322d34afe367eec4210fdee9a555e4ca7"},
+    {file = "ruff-0.0.292-py3-none-manylinux_2_17_ppc64.manylinux2014_ppc64.whl", hash = "sha256:9889bac18a0c07018aac75ef6c1e6511d8411724d67cb879103b01758e110a81"},
+    {file = "ruff-0.0.292-py3-none-manylinux_2_17_ppc64le.manylinux2014_ppc64le.whl", hash = "sha256:6bdfabd4334684a4418b99b3118793f2c13bb67bf1540a769d7816410402a205"},
+    {file = "ruff-0.0.292-py3-none-manylinux_2_17_s390x.manylinux2014_s390x.whl", hash = "sha256:aa7c77c53bfcd75dbcd4d1f42d6cabf2485d2e1ee0678da850f08e1ab13081a8"},
+    {file = "ruff-0.0.292-py3-none-manylinux_2_17_x86_64.manylinux2014_x86_64.whl", hash = "sha256:8e087b24d0d849c5c81516ec740bf4fd48bf363cfb104545464e0fca749b6af9"},
+    {file = "ruff-0.0.292-py3-none-musllinux_1_2_aarch64.whl", hash = "sha256:f160b5ec26be32362d0774964e218f3fcf0a7da299f7e220ef45ae9e3e67101a"},
+    {file = "ruff-0.0.292-py3-none-musllinux_1_2_armv7l.whl", hash = "sha256:ac153eee6dd4444501c4bb92bff866491d4bfb01ce26dd2fff7ca472c8df9ad0"},
+    {file = "ruff-0.0.292-py3-none-musllinux_1_2_i686.whl", hash = "sha256:87616771e72820800b8faea82edd858324b29bb99a920d6aa3d3949dd3f88fb0"},
+    {file = "ruff-0.0.292-py3-none-musllinux_1_2_x86_64.whl", hash = "sha256:b76deb3bdbea2ef97db286cf953488745dd6424c122d275f05836c53f62d4016"},
+    {file = "ruff-0.0.292-py3-none-win32.whl", hash = "sha256:e854b05408f7a8033a027e4b1c7f9889563dd2aca545d13d06711e5c39c3d003"},
+    {file = "ruff-0.0.292-py3-none-win_amd64.whl", hash = "sha256:f27282bedfd04d4c3492e5c3398360c9d86a295be00eccc63914438b4ac8a83c"},
+    {file = "ruff-0.0.292-py3-none-win_arm64.whl", hash = "sha256:7f67a69c8f12fbc8daf6ae6d36705037bde315abf8b82b6e1f4c9e74eb750f68"},
+    {file = "ruff-0.0.292.tar.gz", hash = "sha256:1093449e37dd1e9b813798f6ad70932b57cf614e5c2b5c51005bf67d55db33ac"},
 ]
 
 [[package]]
@@ -3037,13 +3037,13 @@ twisted = "*"
 
 [[package]]
 name = "types-bleach"
-version = "6.0.0.4"
+version = "6.1.0.0"
 description = "Typing stubs for bleach"
 optional = false
-python-versions = "*"
+python-versions = ">=3.7"
 files = [
-    {file = "types-bleach-6.0.0.4.tar.gz", hash = "sha256:357b0226f65c4f20ab3b13ca8d78a6b91c78aad256d8ec168d4e90fc3303ebd4"},
-    {file = "types_bleach-6.0.0.4-py3-none-any.whl", hash = "sha256:2b8767eb407c286b7f02803678732e522e04db8d56cbc9f1270bee49627eae92"},
+    {file = "types-bleach-6.1.0.0.tar.gz", hash = "sha256:3cf0e55d4618890a00af1151f878b2e2a7a96433850b74e12bede7663d774532"},
+    {file = "types_bleach-6.1.0.0-py3-none-any.whl", hash = "sha256:f0bc75d0f6475036ac69afebf37c41d116dfba78dae55db80437caf0fcd35c28"},
 ]
 
 [[package]]
@@ -3444,4 +3444,4 @@ user-search = ["pyicu"]
 [metadata]
 lock-version = "2.0"
 python-versions = "^3.8.0"
-content-hash = "364c309486e9d93d4da8a1a3784d5ecd7d2a9734cf84dcd4a991f2cd54f0b5b5"
+content-hash = "a08543c65f18cc7e9dea648e89c18ab88fc1747aa2e029aa208f777fc3db06dd"
diff --git a/pyproject.toml b/pyproject.toml
index b22172291a..0831510890 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -96,7 +96,7 @@ module-name = "synapse.synapse_rust"
 
 [tool.poetry]
 name = "matrix-synapse"
-version = "1.94.0rc1"
+version = "1.94.0"
 description = "Homeserver for the Matrix decentralised comms protocol"
 authors = ["Matrix.org Team and Contributors <packages@matrix.org>"]
 license = "Apache-2.0"
@@ -321,7 +321,7 @@ all = [
 # This helps prevents merge conflicts when running a batch of dependabot updates.
 isort = ">=5.10.1"
 black = ">=22.7.0"
-ruff = "0.0.290"
+ruff = "0.0.292"
 # Type checking only works with the pydantic.v1 compat module from pydantic v2
 pydantic = "^2"
 
diff --git a/synapse/handlers/device.py b/synapse/handlers/device.py
index 86ad96d030..50df4f2b06 100644
--- a/synapse/handlers/device.py
+++ b/synapse/handlers/device.py
@@ -845,7 +845,6 @@ class DeviceHandler(DeviceWorkerHandler):
                     else:
                         assert max_stream_id == stream_id
                         # Avoid moving `room_id` backwards.
-                        pass
 
                     if self._handle_new_device_update_new_data:
                         continue
diff --git a/synapse/handlers/federation.py b/synapse/handlers/federation.py
index 807a0867cc..9d72794e8b 100644
--- a/synapse/handlers/federation.py
+++ b/synapse/handlers/federation.py
@@ -1497,7 +1497,6 @@ class FederationHandler:
                     # in the meantime and context needs to be recomputed, so let's do so.
                     if i == max_retries - 1:
                         raise e
-                    pass
         else:
             destinations = {x.split(":", 1)[-1] for x in (sender_user_id, room_id)}
 
@@ -1573,7 +1572,6 @@ class FederationHandler:
                 # in the meantime and context needs to be recomputed, so let's do so.
                 if i == max_retries - 1:
                     raise e
-                pass
 
     async def add_display_name_to_third_party_invite(
         self,
diff --git a/synapse/handlers/message.py b/synapse/handlers/message.py
index d0d4626ed6..8de4b8e816 100644
--- a/synapse/handlers/message.py
+++ b/synapse/handlers/message.py
@@ -1129,7 +1129,6 @@ class EventCreationHandler:
                 # in the meantime and context needs to be recomputed, so let's do so.
                 if i == max_retries - 1:
                     raise e
-                pass
 
         # we know it was persisted, so must have a stream ordering
         assert ev.internal_metadata.stream_ordering
@@ -2034,7 +2033,6 @@ class EventCreationHandler:
                         # in the meantime and context needs to be recomputed, so let's do so.
                         if i == max_retries - 1:
                             raise e
-                        pass
                 return True
             except AuthError:
                 logger.info(
diff --git a/synapse/handlers/room.py b/synapse/handlers/room.py
index 4cdf0a8502..97c9f01245 100644
--- a/synapse/handlers/room.py
+++ b/synapse/handlers/room.py
@@ -261,7 +261,6 @@ class RoomCreationHandler:
                 # in the meantime and context needs to be recomputed, so let's do so.
                 if i == max_retries - 1:
                     raise e
-                pass
 
         # This is to satisfy mypy and should never happen
         raise PartialStateConflictError()
diff --git a/synapse/handlers/room_member.py b/synapse/handlers/room_member.py
index 1b50495af1..130eee7e1d 100644
--- a/synapse/handlers/room_member.py
+++ b/synapse/handlers/room_member.py
@@ -500,7 +500,6 @@ class RoomMemberHandler(metaclass=abc.ABCMeta):
                 # in the meantime and context needs to be recomputed, so let's do so.
                 if i == max_retries - 1:
                     raise e
-                pass
 
         # we know it was persisted, so should have a stream ordering
         assert result_event.internal_metadata.stream_ordering
@@ -2005,7 +2004,6 @@ class RoomMemberMasterHandler(RoomMemberHandler):
                 # in the meantime and context needs to be recomputed, so let's do so.
                 if i == max_retries - 1:
                     raise e
-                pass
 
         # we know it was persisted, so must have a stream ordering
         assert result_event.internal_metadata.stream_ordering
diff --git a/synapse/storage/databases/main/account_data.py b/synapse/storage/databases/main/account_data.py
index 16c284807a..39498d52c6 100644
--- a/synapse/storage/databases/main/account_data.py
+++ b/synapse/storage/databases/main/account_data.py
@@ -103,6 +103,13 @@ class AccountDataWorkerStore(PushRulesWorkerStore, CacheInvalidationWorkerStore)
             "AccountDataAndTagsChangeCache", account_max
         )
 
+        self.db_pool.updates.register_background_index_update(
+            update_name="room_account_data_index_room_id",
+            index_name="room_account_data_room_id",
+            table="room_account_data",
+            columns=("room_id",),
+        )
+
         self.db_pool.updates.register_background_update_handler(
             "delete_account_data_for_deactivated_users",
             self._delete_account_data_for_deactivated_users,
diff --git a/synapse/storage/databases/main/e2e_room_keys.py b/synapse/storage/databases/main/e2e_room_keys.py
index bc7c6a6346..aac4cfb054 100644
--- a/synapse/storage/databases/main/e2e_room_keys.py
+++ b/synapse/storage/databases/main/e2e_room_keys.py
@@ -53,6 +53,13 @@ class EndToEndRoomKeyBackgroundStore(SQLBaseStore):
     ):
         super().__init__(database, db_conn, hs)
 
+        self.db_pool.updates.register_background_index_update(
+            update_name="e2e_room_keys_index_room_id",
+            index_name="e2e_room_keys_room_id",
+            table="e2e_room_keys",
+            columns=("room_id",),
+        )
+
         self.db_pool.updates.register_background_update_handler(
             "delete_e2e_backup_keys_for_deactivated_users",
             self._delete_e2e_backup_keys_for_deactivated_users,
diff --git a/synapse/storage/databases/main/purge_events.py b/synapse/storage/databases/main/purge_events.py
index dea0e0458c..1e11bf2706 100644
--- a/synapse/storage/databases/main/purge_events.py
+++ b/synapse/storage/databases/main/purge_events.py
@@ -89,6 +89,11 @@ class PurgeEventsStore(StateGroupWorkerStore, CacheInvalidationWorkerStore):
         # furthermore, we might already have the table from a previous (failed)
         # purge attempt, so let's drop the table first.
 
+        if isinstance(self.database_engine, PostgresEngine):
+            # Disable statement timeouts for this transaction; purging rooms can
+            # take a while!
+            txn.execute("SET LOCAL statement_timeout = 0")
+
         txn.execute("DROP TABLE IF EXISTS events_to_purge")
 
         txn.execute(
diff --git a/synapse/storage/schema/main/delta/82/04_add_indices_for_purging_rooms.sql b/synapse/storage/schema/main/delta/82/04_add_indices_for_purging_rooms.sql
new file mode 100644
index 0000000000..fc948166e6
--- /dev/null
+++ b/synapse/storage/schema/main/delta/82/04_add_indices_for_purging_rooms.sql
@@ -0,0 +1,20 @@
+/* Copyright 2023 The Matrix.org Foundation C.I.C
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *    http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+INSERT INTO background_updates (ordering, update_name, progress_json) VALUES
+    (8204, 'e2e_room_keys_index_room_id', '{}');
+
+INSERT INTO background_updates (ordering, update_name, progress_json) VALUES
+    (8204, 'room_account_data_index_room_id', '{}');