diff --git a/tools/integration.sh b/tools/integration.sh
index 050b54a415..3c4d971a3e 100644
--- a/tools/integration.sh
+++ b/tools/integration.sh
@@ -79,6 +79,16 @@ for PROJECT in $PROJECTS ; do
         # requirements doesn't really install
         continue
     fi
+    if [[ "$BRANCH" =~ "stable" ]]; then
+        # When testing stable, only attempt to sync to projects that also
+        # have a corresponding stable branch.  This prevents us from trying and
+        # failing to sync stable requirements to a library's master branch,
+        # when that same library may be listed and capped in global-requirements.txt.
+        proj_branch="$(cd $REPODIR/$SHORT_PROJECT && git rev-parse --symbolic-full-name --abbrev-ref HEAD)"
+        if [ "$proj_branch" != "$BRANCH" ]; then
+            continue
+        fi
+    fi
 
     # set up the project synced with the global requirements
     sudo chown -R $USER $REPODIR/$SHORT_PROJECT