diff --git a/.zuul.yaml b/.zuul.yaml
index 8ec164acda..7fc7f43b42 100644
--- a/.zuul.yaml
+++ b/.zuul.yaml
@@ -26,6 +26,7 @@
 - job:
     name: glance-tox-oslo-tips-base
     parent: tox
+    abstract: true
     description: Abstract job for Glance vs. oslo libraries
     # NOTE(rosmaita): only need functional test jobs, oslo is
     # already running periodic jobs using our unit tests
@@ -65,6 +66,7 @@
 - job:
     name: glance-tox-keystone-tips-base
     parent: tox
+    abstract: true
     description: Abstract job for Glance vs. keystone
     required-projects:
       - name: openstack/keystoneauth
@@ -106,6 +108,7 @@
 - job:
     name: glance-tox-glance_store-tips-base
     parent: tox
+    abstract: true
     description: Abstract job for Glance vs. glance_store
     required-projects:
       - name: openstack/glance_store
@@ -145,6 +148,7 @@
 - job:
     name: glance-tox-cursive-tips-base
     parent: tox
+    abstract: true
     description: Abstract job for Glance vs. cursive and related libs
     required-projects:
       - name: openstack/cursive
@@ -285,17 +289,43 @@
               - ^tox.ini$
     periodic:
       jobs:
-        - glance-tox-functional-oslo-tips
-        - glance-tox-functional-py35-oslo-tips
-        - glance-tox-py27-keystone-tips
-        - glance-tox-py35-keystone-tips
-        - glance-tox-functional-keystone-tips
-        - glance-tox-functional-py35-keystone-tips
-        - glance-tox-py27-glance_store-tips
-        - glance-tox-py35-glance_store-tips
-        - glance-tox-functional-glance_store-tips
-        - glance-tox-functional-py35-glance_store-tips
-        - glance-tox-py27-cursive-tips
-        - glance-tox-py35-cursive-tips
-        - glance-tox-functional-cursive-tips
-        - glance-tox-functional-py35-cursive-tips
+        # NOTE(rosmaita): we only want the "tips" jobs to be run against
+        # master, hence the 'branches' qualifiers below.  Without them, when
+        # a stable branch is cut, the tests would be run against the stable
+        # branch as well, which is pointless because these libraries are
+        # frozen (more or less) in the stable branches.
+        #
+        # The "tips" jobs can be removed from the stable branch .zuul.yaml
+        # files if someone is so inclined, but that would require manual
+        # maintenance, so we do not do it by default.  Another option is
+        # to define these jobs in the openstack-infra/project-config repo.
+        # That would make us less agile in adjusting these tests, so we
+        # aren't doing that either.
+        - glance-tox-functional-oslo-tips:
+            branches: master
+        - glance-tox-functional-py35-oslo-tips:
+            branches: master
+        - glance-tox-py27-keystone-tips:
+            branches: master
+        - glance-tox-py35-keystone-tips:
+            branches: master
+        - glance-tox-functional-keystone-tips:
+            branches: master
+        - glance-tox-functional-py35-keystone-tips:
+            branches: master
+        - glance-tox-py27-glance_store-tips:
+            branches: master
+        - glance-tox-py35-glance_store-tips:
+            branches: master
+        - glance-tox-functional-glance_store-tips:
+            branches: master
+        - glance-tox-functional-py35-glance_store-tips:
+            branches: master
+        - glance-tox-py27-cursive-tips:
+            branches: master
+        - glance-tox-py35-cursive-tips:
+            branches: master
+        - glance-tox-functional-cursive-tips:
+            branches: master
+        - glance-tox-functional-py35-cursive-tips:
+            branches: master