diff --git a/drivers/docker/driver.go b/drivers/docker/driver.go
index b46190a8f..7c2cd8b1f 100644
--- a/drivers/docker/driver.go
+++ b/drivers/docker/driver.go
@@ -1019,17 +1019,10 @@ func (d *Driver) DestroyTask(taskID string, force bool) error {
 		return fmt.Errorf("must call StopTask for the given task before Destroy or set force to true")
 	}
 
-	defer h.dloggerPluginClient.Kill()
-
 	if err := h.client.StopContainer(h.containerID, 0); err != nil {
 		h.logger.Warn("failed to stop container during destroy", "error", err)
 	}
 
-	if err := h.dlogger.Stop(); err != nil {
-		h.logger.Error("failed to stop docker logger process during destroy",
-			"error", err, "logger_pid", h.dloggerPluginClient.ReattachConfig().Pid)
-	}
-
 	if err := d.cleanupImage(h); err != nil {
 		h.logger.Error("failed to cleanup image after destroying container",
 			"error", err)
diff --git a/drivers/docker/handle.go b/drivers/docker/handle.go
index b1b2c1b5e..219aea403 100644
--- a/drivers/docker/handle.go
+++ b/drivers/docker/handle.go
@@ -156,7 +156,17 @@ func (h *taskHandle) Kill(killTimeout time.Duration, signal os.Signal) error {
 	return nil
 }
 
+func (h *taskHandle) shutdownLogger() {
+	if err := h.dlogger.Stop(); err != nil {
+		h.logger.Error("failed to stop docker logger process during StopTask",
+			"error", err, "logger_pid", h.dloggerPluginClient.ReattachConfig().Pid)
+	}
+	h.dloggerPluginClient.Kill()
+}
+
 func (h *taskHandle) run() {
+	defer h.shutdownLogger()
+
 	exitCode, werr := h.waitClient.WaitContainer(h.containerID)
 	if werr != nil {
 		h.logger.Error("failed to wait for container; already terminated")