diff --git a/heat/engine/cfn/functions.py b/heat/engine/cfn/functions.py
index bc46aea166..dc7fc1906e 100644
--- a/heat/engine/cfn/functions.py
+++ b/heat/engine/cfn/functions.py
@@ -252,7 +252,7 @@ class Select(function.Function):
 
         if (isinstance(strings, collections.Sequence) and
                 not isinstance(strings, six.string_types)):
-            if not isinstance(index, (int, long)):
+            if not isinstance(index, six.integer_types):
                 raise TypeError(_('Index to "%s" must be an integer') %
                                 self.fn_name)
 
@@ -434,7 +434,8 @@ class Replace(function.Function):
                 value = ''
 
             if not isinstance(value,
-                              (six.string_types, int, long, float, bool)):
+                              (six.string_types, six.integer_types,
+                               float, bool)):
                 raise TypeError(_('"%s" params must be strings or numbers') %
                                 self.fn_name)
 
diff --git a/heat/engine/constraints.py b/heat/engine/constraints.py
index 8adbad18ce..4da9ae31b2 100644
--- a/heat/engine/constraints.py
+++ b/heat/engine/constraints.py
@@ -244,7 +244,7 @@ class AnyIndexDict(collections.Mapping):
         self.value = value
 
     def __getitem__(self, key):
-        if key != self.ANYTHING and not isinstance(key, (int, long)):
+        if key != self.ANYTHING and not isinstance(key, six.integer_types):
             raise KeyError(_('Invalid key %s') % str(key))
 
         return self.value
@@ -333,7 +333,7 @@ class Range(Constraint):
         self.max = max
 
         for param in (min, max):
-            if not isinstance(param, (float, int, long, type(None))):
+            if not isinstance(param, (float, six.integer_types, type(None))):
                 raise exception.InvalidSchemaError(
                     message=_('min/max must be numeric'))
 
@@ -402,7 +402,7 @@ class Length(Range):
         super(Length, self).__init__(min, max, description)
 
         for param in (min, max):
-            if not isinstance(param, (int, long, type(None))):
+            if not isinstance(param, (six.integer_types, type(None))):
                 msg = _('min/max length must be integral')
                 raise exception.InvalidSchemaError(message=msg)
 
diff --git a/heat/tests/db/test_migrations.py b/heat/tests/db/test_migrations.py
index 23b3f7d4ff..5a92f20a96 100644
--- a/heat/tests/db/test_migrations.py
+++ b/heat/tests/db/test_migrations.py
@@ -29,6 +29,7 @@ from oslo_db.sqlalchemy import test_base
 from oslo_db.sqlalchemy import test_migrations
 from oslo_db.sqlalchemy import utils
 from oslo_serialization import jsonutils
+import six
 
 from heat.db.sqlalchemy import migrate_repo
 from heat.db.sqlalchemy import migration
@@ -546,12 +547,7 @@ class HeatMigrationsCheckers(test_migrations.WalkVersionsMixin,
         # confirm the resource.id is an int and the uuid field has been
         # copied from the old id.
         for r in res_in_db:
-            # now sqlalchemy returns `long` for mysql
-            # need more convenient way for type check
-            if engine.name == 'mysql':
-                self.assertEqual(long, type(r.id))
-            else:
-                self.assertEqual(int, type(r.id))
+            self.assertIsInstance(r.id, six.integer_types)
             self.assertTrue(uuid_in_res_data(r.uuid))
 
         # confirm that the new resource_id points to the correct resource.