diff --git a/heat/engine/scheduler.py b/heat/engine/scheduler.py
index 36a808ae30..fd2245321b 100644
--- a/heat/engine/scheduler.py
+++ b/heat/engine/scheduler.py
@@ -166,8 +166,8 @@ class TaskRunner(object):
         self.start(timeout=timeout)
         # ensure that zero second sleep is applied only if task
         # has not completed.
-        if not self.done() and wait_time:
-            self._sleep(0)
+        if not self.done():
+            self._sleep(0 if wait_time is not None else None)
         self.run_to_completion(wait_time=wait_time)
 
     def start(self, timeout=None):
@@ -420,7 +420,8 @@ class DependencyTaskGroup(object):
                     if not r:
                         del self._graph[k]
 
-                yield
+                if self._graph:
+                    yield
 
                 for k, r in self._running():
                     if r.step():
diff --git a/heat/tests/test_stack_update.py b/heat/tests/test_stack_update.py
index 2b2d3e86a2..139d3ba3a5 100644
--- a/heat/tests/test_stack_update.py
+++ b/heat/tests/test_stack_update.py
@@ -854,7 +854,7 @@ class StackUpdateTest(common.HeatTestCase):
         tmpl2 = {'HeatTemplateFormatVersion': '2012-12-12',
                  'Resources': {
                      'AResource': {'Type': 'GenericResourceType'},
-                     'BResource': {'Type': 'GenericResourceType'}}}
+                     'BResource': {'Type': 'MultiStepResourceType'}}}
         updated_stack = stack.Stack(self.ctx, 'updated_stack',
                                     template.Template(tmpl2),
                                     disable_rollback=disable_rollback)