diff --git a/jenkins/jobs/python-jobs.yaml b/jenkins/jobs/python-jobs.yaml
index 49551a0981..e3d3565a94 100644
--- a/jenkins/jobs/python-jobs.yaml
+++ b/jenkins/jobs/python-jobs.yaml
@@ -107,6 +107,28 @@
 
     node: '{node}'
 
+- job-template:
+    name: 'gate-{name}-python27-constraints'
+
+    wrappers:
+      - build-timeout:
+          timeout: 50
+      - timestamps
+
+    builders:
+      - revoke-sudo
+      - zuul-git-prep-upper-constraints
+      - tox:
+          envlist: py27-constraints
+      - assert-no-extra-files
+
+    publishers:
+      - test-results
+      - console-log
+      - zuul-swift-test-results-with-console
+
+    node: '{node}'
+
 - job-template:
     name: 'gate-{name}-python34'
 
@@ -128,6 +150,28 @@
 
     node: '{node}'
 
+- job-template:
+    name: 'gate-{name}-python34-constraints'
+
+    wrappers:
+      - build-timeout:
+          timeout: 40
+      - timestamps
+
+    builders:
+      - revoke-sudo
+      - zuul-git-prep-upper-constraints
+      - tox:
+          envlist: py34-constraints
+      - assert-no-extra-files
+
+    publishers:
+      - test-results
+      - console-log
+      - zuul-swift-test-results-with-console
+
+    node: '{node}'
+
 - job-template:
     name: 'gate-{name}-pypy'
 
@@ -149,6 +193,28 @@
 
     node: '{node}'
 
+- job-template:
+    name: 'gate-{name}-pypy-constraints'
+
+    wrappers:
+      - build-timeout:
+          timeout: 40
+      - timestamps
+
+    builders:
+      - revoke-sudo
+      - zuul-git-prep-upper-constraints
+      - tox:
+          envlist: pypy-constraints
+      - assert-no-extra-files
+
+    publishers:
+      - test-results
+      - console-log
+      - zuul-swift-test-results-with-console
+
+    node: '{node}'
+
 - job-template:
     name: 'gate-{name}-docs'
 
@@ -288,3 +354,10 @@
       # pip-missing-reqs isn't standard
       # gate-{name}-tox-{envlist} also isn't standard, but is reserved for
       # projects that want to run specific jobs via tox
+
+- job-group:
+    name: python-constraints-jobs
+    jobs:
+      - 'gate-{name}-python27-constraints'
+      - 'gate-{name}-python34-constraints'
+      - 'gate-{name}-pypy-constraints'
diff --git a/jenkins/scripts/run-tox.sh b/jenkins/scripts/run-tox.sh
index 5c9883cdfe..598a8176ab 100755
--- a/jenkins/scripts/run-tox.sh
+++ b/jenkins/scripts/run-tox.sh
@@ -118,6 +118,7 @@ export NOSE_WITH_XUNIT=1
 export NOSE_WITH_HTML_OUTPUT=1
 export NOSE_HTML_OUT_FILE='nose_results.html'
 export TMPDIR=$(/bin/mktemp -d)
+export UPPER_CONSTRAINTS_FILE=$(pwd)/upper-constraints.txt
 trap "rm -rf $TMPDIR" EXIT
 
 cat /etc/image-hostname.txt
diff --git a/zuul/layout.yaml b/zuul/layout.yaml
index abfafdb750..1bed8fbb13 100755
--- a/zuul/layout.yaml
+++ b/zuul/layout.yaml
@@ -257,6 +257,12 @@ project-templates:
     post:
       - '{name}-branch-tarball'
 
+  - name: python-constraints-jobs
+    check:
+      - 'gate-{name}-python27-constraints'
+    gate:
+      - 'gate-{name}-python27-constraints'
+
   - name: grenade
     check:
       - 'gate-grenade-dsvm'
@@ -310,6 +316,12 @@ project-templates:
     gate:
       - 'gate-{name}-python34'
 
+  - name: python3-constraints-jobs
+    check:
+      - 'gate-{name}-python34-constraints'
+    gate:
+      - 'gate-{name}-python34-constraints'
+
   # Python 2.6 is deprecated, these jobs will be removed once no
   # OpenStack projects needs it (once Juno is retired).
   - name: python26-jobs
@@ -326,6 +338,12 @@ project-templates:
     # gate:
     #  - 'gate-{name}-pypy'
 
+  - name: pypy-constraints-jobs
+    check:
+      - 'gate-{name}-pypy-constraints'
+    gate:
+      - 'gate-{name}-pypy-constraints'
+
   - name: openstack-server-publish-jobs
     post:
       - '{name}-docs'
@@ -1717,6 +1735,12 @@ jobs:
   - name: gate-tempest-dsvm-neutron-large-ops-liberty
     branch: master
 
+  # Constraints Jobs
+  - name: ^gate-.*-py(?:thon\d\d|py)-constraints$
+    branch: ^(?!stable/(?:juno|kilo)).*$
+
+  # End Constraints Jobs
+
 # The project list is grouped by type of project, and within each
 # group, projects are sorted (mostly) alphabetically.
 projects: