diff --git a/common/docker/client.go b/common/docker/client.go
index 00100186..f85e53b1 100644
--- a/common/docker/client.go
+++ b/common/docker/client.go
@@ -165,13 +165,25 @@ func (pending pendingStarts) finish(id string) {
 	}
 }
 
+// AllContainerIDs returns all the IDs of Docker containers,
+// whether they are running or not.
 func (c *Client) AllContainerIDs() ([]string, error) {
-	all, err := c.ListContainers(docker.ListContainersOptions{All: true})
+	return c.containerIDs(true)
+}
+
+// RunningContainerIDs returns all the IDs of the running
+// Docker containers.
+func (c *Client) RunningContainerIDs() ([]string, error) {
+	return c.containerIDs(false)
+}
+
+func (c *Client) containerIDs(all bool) ([]string, error) {
+	containers, err := c.ListContainers(docker.ListContainersOptions{All: all})
 	if err != nil {
 		return nil, err
 	}
 	var ids []string
-	for _, c := range all {
+	for _, c := range containers {
 		ids = append(ids, c.ID)
 	}
 	return ids, nil
diff --git a/prog/weaver/main.go b/prog/weaver/main.go
index f2666188..231c157a 100644
--- a/prog/weaver/main.go
+++ b/prog/weaver/main.go
@@ -307,11 +307,15 @@ func main() {
 			trackerName = "awsvpc"
 		}
 		var allContainerIDs []string
+		var runningContainerIDs []string
 		if dockerCli != nil {
 			allContainerIDs, err = dockerCli.AllContainerIDs()
 			checkFatal(err)
+
+			runningContainerIDs, err = dockerCli.RunningContainerIDs()
+			checkFatal(err)
 		}
-		preClaims, err := findExistingAddresses(dockerCli, allContainerIDs, weavenet.WeaveBridgeName)
+		preClaims, err := findExistingAddresses(dockerCli, runningContainerIDs, weavenet.WeaveBridgeName)
 		checkFatal(err)
 		allocator, defaultSubnet = createAllocator(router, ipamConfig, preClaims, db, t, isKnownPeer)
 		observeContainers(allocator)