diff --git a/roles/run-tempest/README.rst b/roles/run-tempest/README.rst
index f9fcf28d29..0c72b69a54 100644
--- a/roles/run-tempest/README.rst
+++ b/roles/run-tempest/README.rst
@@ -81,7 +81,7 @@ variable (through the `register` statement).
 .. zuul:rolevar:: stable_constraints_file
    :default: ''
 
-   Upper constraints file to be used for stable branch till stable/rocky.
+   Upper constraints file to be used for stable branch till stable/stein.
 
 .. zuul:rolevar:: tempest_tox_environment
    :default: ''
diff --git a/roles/run-tempest/tasks/main.yaml b/roles/run-tempest/tasks/main.yaml
index 999e256583..5b00de3402 100644
--- a/roles/run-tempest/tasks/main.yaml
+++ b/roles/run-tempest/tasks/main.yaml
@@ -25,11 +25,11 @@
     target_branch: "{{ zuul.override_checkout }}"
   when: zuul.override_checkout is defined
 
-- name: Use stable branch upper-constraints till stable/rocky
+- name: Use stable branch upper-constraints till stable/stein
   set_fact:
     # TOX_CONSTRAINTS_FILE is new name, UPPER_CONSTRAINTS_FILE is old one, best to set both
     tempest_tox_environment: "{{ tempest_tox_environment | combine({'UPPER_CONSTRAINTS_FILE': stable_constraints_file}) | combine({'TOX_CONSTRAINTS_FILE': stable_constraints_file}) }}"
-  when: target_branch in ["stable/ocata", "stable/pike", "stable/queens", "stable/rocky"]
+  when: target_branch in ["stable/ocata", "stable/pike", "stable/queens", "stable/rocky", "stable/stein"]
 
 - name: Set OS_TEST_TIMEOUT if requested
   set_fact: