diff --git a/.zuul.yaml b/.zuul.yaml
index d3fda4165ee4..b9e0213b3f59 100644
--- a/.zuul.yaml
+++ b/.zuul.yaml
@@ -165,7 +165,7 @@
       TLS console proxy code in the libvirt driver.
       Starting in Stein, the job was changed to run with python 3 and enabled
       volume multi-attach testing.
-      Runs all tempest compute API and scenario tests concurrently.
+      Runs all tempest compute API and most scenario tests concurrently.
     run: playbooks/legacy/nova-next/run.yaml
     post-run: playbooks/legacy/nova-next/post.yaml
 
diff --git a/playbooks/legacy/nova-next/run.yaml b/playbooks/legacy/nova-next/run.yaml
index 8c3e7dd4494c..1005b616aa35 100644
--- a/playbooks/legacy/nova-next/run.yaml
+++ b/playbooks/legacy/nova-next/run.yaml
@@ -60,9 +60,12 @@
           export PYTHONUNBUFFERED=true
           # Yes we want to run Tempest.
           export DEVSTACK_GATE_TEMPEST=1
-          # Run all compute API tests and all scenario tests at the default
+          # Run all compute API tests and most scenario tests at the default
           # concurrency (nproc/2 which is normally 4 in the gate).
-          export DEVSTACK_GATE_TEMPEST_REGEX="^tempest\.((scenario)|(api\.compute))"
+          # The tempest.scenario.test_network* tests are skipped because they
+          # (1) take a long time and (2) are already covered in the
+          # tempest-slow* job.
+          export DEVSTACK_GATE_TEMPEST_REGEX="^tempest\.((scenario(?!\.test_network))|(api\.compute))"
           # The post_test_hook runs some post-test CLIs for things that
           # Tempest does not test, like archiving deleted records.
           function post_test_hook {