diff --git a/test/integration/targets/incidental_inventory_docker_swarm/playbooks/swarm_cleanup.yml b/test/integration/targets/incidental_inventory_docker_swarm/playbooks/swarm_cleanup.yml
index 9cf87159c6f..fc4455ec7c5 100644
--- a/test/integration/targets/incidental_inventory_docker_swarm/playbooks/swarm_cleanup.yml
+++ b/test/integration/targets/incidental_inventory_docker_swarm/playbooks/swarm_cleanup.yml
@@ -15,4 +15,5 @@
           - docker
           - docker-ce
           - docker-ce-cli
+          - containerd.io
         state: absent
diff --git a/test/integration/targets/incidental_setup_docker/defaults/main.yml b/test/integration/targets/incidental_setup_docker/defaults/main.yml
index f7be73dc0e0..48959cc3ec7 100644
--- a/test/integration/targets/incidental_setup_docker/defaults/main.yml
+++ b/test/integration/targets/incidental_setup_docker/defaults/main.yml
@@ -7,6 +7,7 @@ docker_packages:
   - docker-ce
 
 docker_pip_extra_packages: []
+docker_pip_never_remove: []
 docker_pip_packages:
   - docker
 
@@ -14,3 +15,4 @@ docker_cleanup_packages:
   - docker
   - docker-ce
   - docker-ce-cli
+  - containerd.io
diff --git a/test/integration/targets/incidental_setup_docker/handlers/main.yml b/test/integration/targets/incidental_setup_docker/handlers/main.yml
index 93d9657cbb7..9e3f928f481 100644
--- a/test/integration/targets/incidental_setup_docker/handlers/main.yml
+++ b/test/integration/targets/incidental_setup_docker/handlers/main.yml
@@ -1,11 +1,11 @@
 - name: remove pip packages
   pip:
-    state: present
-    name: "{{ docker_pip_packages | union(docker_pip_extra_packages) }}"
+    state: absent
+    name: "{{ docker_pip_packages | union(docker_pip_extra_packages) | difference(docker_pip_never_remove) }}"
   listen: cleanup docker
   when: not docker_skip_cleanup | bool
 
-- name: remove docker pagkages
+- name: remove docker packages
   action: "{{ ansible_facts.pkg_mgr }}"
   args:
     name: "{{ docker_cleanup_packages }}"
diff --git a/test/integration/targets/incidental_setup_docker/vars/RedHat-7.yml b/test/integration/targets/incidental_setup_docker/vars/RedHat-7.yml
index bc1c7820906..84ba0920880 100644
--- a/test/integration/targets/incidental_setup_docker/vars/RedHat-7.yml
+++ b/test/integration/targets/incidental_setup_docker/vars/RedHat-7.yml
@@ -10,3 +10,9 @@ docker_packages:
 
 docker_pip_extra_packages:
   - requests==2.6.0
+
+# We need to pin the above so pip finds the right system-installed package
+# but we never want to try to remove it, so we substract this from the set of
+# packages we remove on cleanup
+docker_pip_never_remove:
+  - requests==2.6.0