diff --git a/heat/db/sqlalchemy/migrate_repo/versions/056_convergence_parameter_storage.py b/heat/db/sqlalchemy/migrate_repo/versions/056_convergence_parameter_storage.py
index 74ae04419c..69318f987d 100644
--- a/heat/db/sqlalchemy/migrate_repo/versions/056_convergence_parameter_storage.py
+++ b/heat/db/sqlalchemy/migrate_repo/versions/056_convergence_parameter_storage.py
@@ -41,8 +41,8 @@ def upgrade(migrate_engine):
     stack_table = sqlalchemy.Table('stack', meta, autoload=True)
     update_query = tmpl_table.update().values(
         environment=sqlalchemy.select([stack_table.c.parameters]).
-        where(tmpl_table.c.id == stack_table.c.raw_template_id).
-        as_scalar())
+        where(sqlalchemy.and_(stack_table.c.raw_template_id == tmpl_table.c.id,
+                              stack_table.c.deleted_at.is_(None))).as_scalar())
     migrate_engine.execute(update_query)
 
     stack_table.c.parameters.drop()
@@ -76,14 +76,16 @@ def upgrade_sqlite(migrate_engine):
 
     stack_parameters = {}
     for s in stacks:
-        stack_parameters[s.raw_template_id] = s.parameters
+        stack_parameters[s.raw_template_id] = (s.parameters, s.deleted_at)
 
     colnames = [c.name for c in tmpl_table.columns]
     for template in templates:
         values = dict(zip(colnames,
                           map(lambda colname: getattr(template, colname),
                               colnames)))
-        values['environment'] = stack_parameters.get(values['id'])
+        params, del_at = stack_parameters.get(values['id'], (None, None))
+        if params is not None and del_at is None:
+            values['environment'] = params
         migrate_engine.execute(new_template.insert(values))
 
     # migrate stacks to new table
diff --git a/heat/tests/db/test_migrations.py b/heat/tests/db/test_migrations.py
index 02ab041d6d..69a4f1251f 100644
--- a/heat/tests/db/test_migrations.py
+++ b/heat/tests/db/test_migrations.py
@@ -434,11 +434,11 @@ class HeatMigrationsCheckers(test_migrations.WalkVersionsMixin,
             templ.append(t)
 
         user_creds = utils.get_table(engine, 'user_creds')
-        user = [dict(id=900, username='test_user', password='password',
+        user = [dict(id=uid, username='test_user', password='password',
                      tenant='test_project', auth_url='bla',
                      tenant_id=str(uuid.uuid4()),
                      trust_id='',
-                     trustor_user_id='')]
+                     trustor_user_id='') for uid in range(900, 903)]
         engine.execute(user_creds.insert(), user)
 
         stack = utils.get_table(engine, 'stack')
@@ -447,11 +447,14 @@ class HeatMigrationsCheckers(test_migrations.WalkVersionsMixin,
                      ('9a4bd1e9-8b21-46cd-964a-f66cb1cfa2f9', 2)]
         data = [dict(id=ll_id, name=ll_id,
                      raw_template_id=templ[templ_id]['id'],
-                     user_creds_id=user[0]['id'],
+                     user_creds_id=user[templ_id]['id'],
                      username='test_user',
                      disable_rollback=True,
-                     parameters='test_params')
+                     parameters='test_params',
+                     created_at=datetime.datetime.utcnow(),
+                     deleted_at=None)
                 for ll_id, templ_id in stack_ids]
+        data[-1]['deleted_at'] = datetime.datetime.utcnow()
 
         engine.execute(stack.insert(), data)
         return data
@@ -465,23 +468,29 @@ class HeatMigrationsCheckers(test_migrations.WalkVersionsMixin,
         # Get the parameters in stack table
         stack_parameters = {}
         for stack in data:
-            stack_parameters[stack['raw_template_id']] = stack['parameters']
+            templ_id = stack['raw_template_id']
+            stack_parameters[templ_id] = (stack['parameters'],
+                                          stack.get('deleted_at'))
 
         # validate whether its moved to raw_template
         raw_template_table = utils.get_table(engine, 'raw_template')
         raw_templates = raw_template_table.select().execute()
 
         for raw_template in raw_templates:
-            if stack_parameters.get(raw_template.id) is not None:
-                stack_param = stack_parameters[raw_template.id]
+            if raw_template.id in stack_parameters:
+                stack_param, deleted_at = stack_parameters[raw_template.id]
                 tmpl_env = raw_template.environment
-                if engine.name == 'sqlite':
+                if engine.name == 'sqlite' and deleted_at is None:
                     stack_param = '"%s"' % stack_param
-
-                self.assertEqual(stack_param,
-                                 tmpl_env,
-                                 'parameters migration from stack to '
-                                 'raw_template failed')
+                if deleted_at is None:
+                    self.assertEqual(stack_param,
+                                     tmpl_env,
+                                     'parameters migration from stack to '
+                                     'raw_template failed')
+                else:
+                    self.assertIsNone(tmpl_env,
+                                      'parameters migration did not skip '
+                                      'deleted stack')
 
     def _pre_upgrade_057(self, engine):
         # template