diff --git a/changelog.d/12637.misc b/changelog.d/12637.misc
new file mode 100644
index 0000000000..735257787f
--- /dev/null
+++ b/changelog.d/12637.misc
@@ -0,0 +1 @@
+Minor improvements to the scripts for running Synapse in worker mode under Complement.
diff --git a/docker/conf-workers/supervisord.conf.j2 b/docker/conf-workers/supervisord.conf.j2
index 408ef72787..ca1f7aef8e 100644
--- a/docker/conf-workers/supervisord.conf.j2
+++ b/docker/conf-workers/supervisord.conf.j2
@@ -9,7 +9,7 @@ user=root
 files = /etc/supervisor/conf.d/*.conf
 
 [program:nginx]
-command=/usr/sbin/nginx -g "daemon off;"
+command=/usr/local/bin/prefix-log /usr/sbin/nginx -g "daemon off;"
 priority=500
 stdout_logfile=/dev/stdout
 stdout_logfile_maxbytes=0
@@ -19,7 +19,7 @@ username=www-data
 autorestart=true
 
 [program:redis]
-command=/usr/bin/redis-server /etc/redis/redis.conf --daemonize no
+command=/usr/local/bin/prefix-log /usr/bin/redis-server /etc/redis/redis.conf --daemonize no
 priority=1
 stdout_logfile=/dev/stdout
 stdout_logfile_maxbytes=0
@@ -29,7 +29,7 @@ username=redis
 autorestart=true
 
 [program:synapse_main]
-command=/usr/local/bin/python -m synapse.app.homeserver --config-path="{{ main_config_path }}" --config-path=/conf/workers/shared.yaml
+command=/usr/local/bin/prefix-log /usr/local/bin/python -m synapse.app.homeserver --config-path="{{ main_config_path }}" --config-path=/conf/workers/shared.yaml
 priority=10
 # Log startup failures to supervisord's stdout/err
 # Regular synapse logs will still go in the configured data directory
diff --git a/scripts-dev/complement.sh b/scripts-dev/complement.sh
index e0feba05fa..190df6909a 100755
--- a/scripts-dev/complement.sh
+++ b/scripts-dev/complement.sh
@@ -43,6 +43,8 @@ fi
 # Build the base Synapse image from the local checkout
 docker build -t matrixdotorg/synapse -f "docker/Dockerfile" .
 
+extra_test_args=()
+
 # If we're using workers, modify the docker files slightly.
 if [[ -n "$WORKERS" ]]; then
   # Build the workers docker image (from the base Synapse image).
@@ -52,7 +54,14 @@ if [[ -n "$WORKERS" ]]; then
   COMPLEMENT_DOCKERFILE=SynapseWorkers.Dockerfile
 
   # And provide some more configuration to complement.
-  export COMPLEMENT_SPAWN_HS_TIMEOUT_SECS=60
+
+  # It can take quite a while to spin up a worker-mode Synapse for the first
+  # time (the main problem is that we start 14 python processes for each test,
+  # and complement likes to do two of them in parallel).
+  export COMPLEMENT_SPAWN_HS_TIMEOUT_SECS=120
+
+  # ... and it takes longer than 10m to run the whole suite.
+  extra_test_args+=("-timeout=60m")
 else
   export COMPLEMENT_BASE_IMAGE=complement-synapse
   COMPLEMENT_DOCKERFILE=Dockerfile
@@ -64,4 +73,4 @@ docker build -t $COMPLEMENT_BASE_IMAGE -f "docker/complement/$COMPLEMENT_DOCKERF
 # Run the tests!
 echo "Images built; running complement"
 cd "$COMPLEMENT_DIR"
-go test -v -tags synapse_blacklist,msc2716,msc3030,faster_joins -count=1 "$@" ./tests/...
+go test -v -tags synapse_blacklist,msc2716,msc3030,faster_joins -count=1 "${extra_test_args[@]}" "$@" ./tests/...