diff --git a/test/335_rmpeer_3_test.sh b/test/335_rmpeer_3_test.sh
index ffdfc85b..eb8f916e 100755
--- a/test/335_rmpeer_3_test.sh
+++ b/test/335_rmpeer_3_test.sh
@@ -14,7 +14,10 @@ weave_on $HOST3 launch $HOST1
 weave_on $HOST3 prime
 
 # nuke 1st peer
-docker_on $HOST1 kill weave
+# NOTE: docker-kill hangs (https://github.com/docker/docker/issues/31447), so we
+# kill directly the weaver process instead.
+WEAVER_PID=$(container_pid $HOST1 weave)
+run_on $HOST1 "sudo kill -9 $WEAVER_PID"
 
 # transfer its space to the 2nd
 weave_on $HOST2 rmpeer $PEER1
diff --git a/test/620_proxy_entrypoint_command_test.sh b/test/620_proxy_entrypoint_command_test.sh
index 1085bcac..748c415a 100755
--- a/test/620_proxy_entrypoint_command_test.sh
+++ b/test/620_proxy_entrypoint_command_test.sh
@@ -15,7 +15,7 @@ run_container() {
 }
 
 start_suite "Proxy uses correct entrypoint and command with weavewait"
-weave_on $HOST1 launch-proxy
+weave_on $HOST1 launch-proxy --no-restart
 
 build_image check-ethwe-up '["grep"]' '["^1$", "/sys/class/net/ethwe/carrier"]'
 run_container "check-ethwe-up"
@@ -27,7 +27,11 @@ build_image false '["/bin/false"]' ''
 run_container "--entrypoint='grep' false ^1$ /sys/class/net/ethwe/carrier"
 
 weave_on $HOST1 launch-router --ipalloc-range 10.2.2.0/24
-docker_on $HOST1 kill weaveproxy
+# NOTE: docker-kill hangs (https://github.com/docker/docker/issues/31447), so we
+# kill directly the weaveproxy process instead.
+WEAVEPROXY_PID=$(container_pid $HOST1 weaveproxy)
+$SSH $HOST1 "ps aux | grep weaveproxy"
+run_on $HOST1 "sudo kill -9 $WEAVEPROXY_PID"
 weave_on $HOST1 launch-proxy
 
 assert_raises "proxy docker_on $HOST1 run check-ethwe-up"