diff --git a/zuul.d/project-templates.yaml b/zuul.d/project-templates.yaml
index d8876f5e..d2e9cf32 100644
--- a/zuul.d/project-templates.yaml
+++ b/zuul.d/project-templates.yaml
@@ -286,6 +286,38 @@
         - openstack-tox-py35:
             voting: false
 
+- project-template:
+    name: openstack-python-jobs-no-constraints
+    description: |
+      Runs the OpenStack PTI jobs for python, but uses the versions of them
+      that do not use constraints.
+    check:
+      jobs:
+        - tox-pep8
+        - tox-py27
+    gate:
+      jobs:
+        - tox-pep8
+        - tox-py27
+    post:
+      jobs:
+        - publish-openstack-python-branch-tarball
+
+- project-template:
+    name: openstack-python35-jobs-no-constraints
+    description: |
+      Runs the OpenStack PTI jobs for python3.5, but uses the versions of them
+      that do not use constraints.
+    check:
+      jobs:
+        - tox-py35
+    gate:
+      jobs:
+        - tox-py35
+    post:
+      jobs:
+        - publish-openstack-python-branch-tarball
+
 - project-template:
     name: openstack-pypy-jobs
     check: