diff --git a/playbooks/publish/wheel-mirror.yaml b/playbooks/publish/wheel-mirror.yaml
index 8babfa5591..7531d8a4a0 100644
--- a/playbooks/publish/wheel-mirror.yaml
+++ b/playbooks/publish/wheel-mirror.yaml
@@ -1,5 +1,5 @@
 - hosts: all
-  strategy: free
+  strategy: linear
 
   pre_tasks:
     - name: Generate AFS slug - CentOS
diff --git a/roles/copy-wheels/tasks/main.yaml b/roles/copy-wheels/tasks/main.yaml
index cc3dccd24b..cd9adc870c 100644
--- a/roles/copy-wheels/tasks/main.yaml
+++ b/roles/copy-wheels/tasks/main.yaml
@@ -3,3 +3,7 @@
 
 - name: Rebuild mirror index
   script: wheel-index.sh {{ afs_dir }}
+  # With multiple python2/3 builds, we only need one host to generate
+  # the final index.  All hosts should be finished copying under
+  # linear strategy.
+  run_once: True