diff --git a/contrib/completion/bash/docker b/contrib/completion/bash/docker
index b40fc4141d..48ebc69224 100644
--- a/contrib/completion/bash/docker
+++ b/contrib/completion/bash/docker
@@ -156,6 +156,11 @@ __docker_complete_containers_running() {
 	__docker_complete_containers "$@" --filter status=running
 }
 
+# shellcheck disable=SC2120
+__docker_complete_containers_stoppable() {
+	__docker_complete_containers "$@" --filter status=running --filter status=paused
+}
+
 # shellcheck disable=SC2120
 __docker_complete_containers_stopped() {
 	__docker_complete_containers "$@" --filter status=exited
@@ -2176,7 +2181,7 @@ _docker_container_stop() {
 			COMPREPLY=( $( compgen -W "--help --time -t" -- "$cur" ) )
 			;;
 		*)
-			__docker_complete_containers_running
+			__docker_complete_containers_stoppable
 			;;
 	esac
 }