diff --git a/modules/docker.nix b/modules/docker.nix
index 89e8cb7..8d7e470 100644
--- a/modules/docker.nix
+++ b/modules/docker.nix
@@ -28,6 +28,7 @@
 #      };
 
       # Run `docker system prune -f ${autoPrune.flags}` every week.
+      # This creates `docker-prune.service` and `docker-prune.timer`.
       autoPrune.enable = true;
       autoPrune.dates = "weekly";
       # https://docs.docker.com/engine/reference/commandline/system_prune/#options
@@ -54,9 +55,17 @@
     script = ''
       ${pkgs.docker}/bin/docker system prune -f --all --volumes
     '';
+
+    # Run weekly after `docker-prune.service` has finished.
+    # Reason: Only one `docker system prune` command can be run at a time.
+
     startAt = "weekly";
-    after = [ "docker.service" ];
+    # Start the specified units when this unit is started,
+    # and stop this unit when the specified units are stopped or fail.
     requires = [ "docker.service" ];
+    # If the specified units are started at the same time as this unit,
+    # delay this unit until they have started.
+    after = [ "docker.service" "docker-prune.service" ];
   };
 
   # Monitor unhealthy Docker containers.