diff --git a/changelog.d/13279.misc b/changelog.d/13279.misc
new file mode 100644
index 0000000000..a083d2af2a
--- /dev/null
+++ b/changelog.d/13279.misc
@@ -0,0 +1 @@
+Reduce the rebuild time for the complement-synapse docker image.
diff --git a/docker/complement/Dockerfile b/docker/complement/Dockerfile
index 8bec0f6116..c5e7984a28 100644
--- a/docker/complement/Dockerfile
+++ b/docker/complement/Dockerfile
@@ -4,42 +4,58 @@
 #
 # Instructions for building this image from those it depends on is detailed in this guide:
 # https://github.com/matrix-org/synapse/blob/develop/docker/README-testing.md#testing-with-postgresql-and-single-or-multi-process-synapse
+
 ARG SYNAPSE_VERSION=latest
+
+# first of all, we create a base image with a postgres server and database,
+# which we can copy into the target image. For repeated rebuilds, this is
+# much faster than apt installing postgres each time.
+#
+# This trick only works because (a) the Synapse image happens to have all the
+# shared libraries that postgres wants, (b) we use a postgres image based on
+# the same debian version as Synapse's docker image (so the versions of the
+# shared libraries match).
+
+FROM postgres:13-bullseye AS postgres_base
+    # initialise the database cluster in /var/lib/postgresql
+    RUN gosu postgres initdb --locale=C --encoding=UTF-8 --auth-host password
+
+    # Configure a password and create a database for Synapse
+    RUN echo "ALTER USER postgres PASSWORD 'somesecret'" | gosu postgres postgres --single
+    RUN echo "CREATE DATABASE synapse" | gosu postgres postgres --single
+
+# now build the final image, based on the Synapse image.
+
 FROM matrixdotorg/synapse-workers:$SYNAPSE_VERSION
+    # copy the postgres installation over from the image we built above
+    RUN adduser --system --uid 999 postgres --home /var/lib/postgresql
+    COPY --from=postgres_base /var/lib/postgresql /var/lib/postgresql
+    COPY --from=postgres_base /usr/lib/postgresql /usr/lib/postgresql
+    COPY --from=postgres_base /usr/share/postgresql /usr/share/postgresql
+    RUN mkdir /var/run/postgresql && chown postgres /var/run/postgresql
+    ENV PATH="${PATH}:/usr/lib/postgresql/13/bin"
+    ENV PGDATA=/var/lib/postgresql/data
 
-# Install postgresql
-RUN apt-get update && \
-  DEBIAN_FRONTEND=noninteractive apt-get install --no-install-recommends -yqq postgresql-13
+    # Extend the shared homeserver config to disable rate-limiting,
+    # set Complement's static shared secret, enable registration, amongst other
+    # tweaks to get Synapse ready for testing.
+    # To do this, we copy the old template out of the way and then include it
+    # with Jinja2.
+    RUN mv /conf/shared.yaml.j2 /conf/shared-orig.yaml.j2
+    COPY conf/workers-shared-extra.yaml.j2 /conf/shared.yaml.j2
 
-# Configure a user and create a database for Synapse
-RUN pg_ctlcluster 13 main start &&  su postgres -c "echo \
- \"ALTER USER postgres PASSWORD 'somesecret'; \
- CREATE DATABASE synapse \
-  ENCODING 'UTF8' \
-  LC_COLLATE='C' \
-  LC_CTYPE='C' \
-  template=template0;\" | psql" && pg_ctlcluster 13 main stop
+    WORKDIR /data
 
-# Extend the shared homeserver config to disable rate-limiting,
-# set Complement's static shared secret, enable registration, amongst other
-# tweaks to get Synapse ready for testing.
-# To do this, we copy the old template out of the way and then include it
-# with Jinja2.
-RUN mv /conf/shared.yaml.j2 /conf/shared-orig.yaml.j2
-COPY conf/workers-shared-extra.yaml.j2 /conf/shared.yaml.j2
+    COPY conf/postgres.supervisord.conf /etc/supervisor/conf.d/postgres.conf
 
-WORKDIR /data
+    # Copy the entrypoint
+    COPY conf/start_for_complement.sh /
 
-COPY conf/postgres.supervisord.conf /etc/supervisor/conf.d/postgres.conf
+    # Expose nginx's listener ports
+    EXPOSE 8008 8448
 
-# Copy the entrypoint
-COPY conf/start_for_complement.sh /
+    ENTRYPOINT ["/start_for_complement.sh"]
 
-# Expose nginx's listener ports
-EXPOSE 8008 8448
-
-ENTRYPOINT ["/start_for_complement.sh"]
-
-# Update the healthcheck to have a shorter check interval
-HEALTHCHECK --start-period=5s --interval=1s --timeout=1s \
-    CMD /bin/sh /healthcheck.sh
+    # Update the healthcheck to have a shorter check interval
+    HEALTHCHECK --start-period=5s --interval=1s --timeout=1s \
+        CMD /bin/sh /healthcheck.sh
diff --git a/docker/complement/conf/postgres.supervisord.conf b/docker/complement/conf/postgres.supervisord.conf
index 5dae3e6330..b88bfc772e 100644
--- a/docker/complement/conf/postgres.supervisord.conf
+++ b/docker/complement/conf/postgres.supervisord.conf
@@ -1,5 +1,5 @@
 [program:postgres]
-command=/usr/local/bin/prefix-log /usr/bin/pg_ctlcluster 13 main start --foreground
+command=/usr/local/bin/prefix-log gosu postgres postgres
 
 # Only start if START_POSTGRES=1
 autostart=%(ENV_START_POSTGRES)s