diff --git a/zuul.d/project-templates.yaml b/zuul.d/project-templates.yaml
index bcfcfd7e..cb05e90f 100644
--- a/zuul.d/project-templates.yaml
+++ b/zuul.d/project-templates.yaml
@@ -919,6 +919,23 @@
       jobs:
         - publish-openstack-python-branch-tarball
 
+- project-template:
+    name: openstack-python37-jobs-no-constraints
+    description: |
+      Runs the OpenStack PTI jobs for python3.7, but uses the versions of them
+      that do not use constraints.
+    check:
+      jobs:
+        - tox-pep8
+        - tox-py37
+    gate:
+      jobs:
+        - tox-pep8
+        - tox-py37
+    post:
+      jobs:
+        - publish-openstack-python-branch-tarball
+
 - project-template:
     name: openstack-lower-constraints-jobs
     description: |