diff --git a/tox.ini b/tox.ini
index e1c17df..d5b41af 100644
--- a/tox.ini
+++ b/tox.ini
@@ -289,6 +289,18 @@
     find . -type f -name "*.pyc" -delete
     tempest run --serial --regex {[testenv:slow-serial]regex} {posargs}
 
+[testenv:slow]
+envdir = .tox/tempest
+sitepackages = {[tempestenv]sitepackages}
+basepython = {[tempestenv]basepython}
+setenv = {[tempestenv]setenv}
+deps = {[tempestenv]deps}
+# The regex below is used to select the slow tagged tests:
+regex = '\[.*\bslow\b.*\]'
+commands =
+    find . -type f -name "*.pyc" -delete
+    tempest run --regex {[testenv:slow]regex} {posargs}
+
 [testenv:ipv6-only]
 envdir = .tox/tempest
 sitepackages = {[tempestenv]sitepackages}
diff --git a/zuul.d/integrated-gate.yaml b/zuul.d/integrated-gate.yaml
index f379041..a67f6b4 100644
--- a/zuul.d/integrated-gate.yaml
+++ b/zuul.d/integrated-gate.yaml
@@ -294,6 +294,13 @@
     vars: *tempest_slow_vars
 
 - job:
+    name: tempest-slow-parallel
+    parent: tempest-slow-py3
+    # This job run slow tests in parallel.
+    vars:
+      tox_envlist: slow
+
+- job:
     name: tempest-cinder-v2-api
     parent: devstack-tempest
     # NOTE(gmann): Cinder v2 APIs are available until
diff --git a/zuul.d/project.yaml b/zuul.d/project.yaml
index 9d2ec88..126119b 100644
--- a/zuul.d/project.yaml
+++ b/zuul.d/project.yaml
@@ -11,7 +11,7 @@
         - openstack-tox-py38
         - openstack-tox-py39
         - openstack-tox-py310
-        - tempest-full-parallel:
+        - tempest-full-py3:
             # Define list of irrelevant files to use everywhere else
             irrelevant-files: &tempest-irrelevant-files
               - ^.*\.rst$
@@ -26,8 +26,6 @@
               - ^.gitignore$
               - ^.gitreview$
               - ^.mailmap$
-        - tempest-full-py3:
-            irrelevant-files: *tempest-irrelevant-files
         - tempest-full-ubuntu-focal:
             irrelevant-files: *tempest-irrelevant-files
         - glance-multistore-cinder-import:
@@ -182,6 +180,8 @@
     periodic:
       jobs:
         - tempest-all
+        - tempest-slow-parallel
+        - tempest-full-parallel
         - tempest-full-oslo-master
         - tempest-stestr-master
         - tempest-full-py3-ipv6
diff --git a/zuul.d/tempest-specific.yaml b/zuul.d/tempest-specific.yaml
index ca9ba7f..684270a 100644
--- a/zuul.d/tempest-specific.yaml
+++ b/zuul.d/tempest-specific.yaml
@@ -34,7 +34,6 @@
 - job:
     name: tempest-full-parallel
     parent: tempest-full-py3
-    voting: false
     branches:
       - master
     description: |