diff --git a/.packit.yaml b/.packit.yaml
index 4e3418f..fb45e37 100644
--- a/.packit.yaml
+++ b/.packit.yaml
@@ -49,13 +49,13 @@ jobs:
       - fedora-rawhide-x86_64
       - fedora-40-x86_64
       - fedora-39-x86_64
-    identifier: docker
-    tmt_plan: /tests/docker
-
-  - <<: *tests
     identifier: podman
     tmt_plan: /tests/podman
 
   - <<: *tests
     identifier: rootful-podman
     tmt_plan: /tests/rootful-podman
+
+  - <<: *tests
+    identifier: docker
+    tmt_plan: /tests/docker
diff --git a/plans/tests.fmf b/plans/tests.fmf
index c98e0fd..09028e2 100644
--- a/plans/tests.fmf
+++ b/plans/tests.fmf
@@ -44,11 +44,6 @@ execute:
     tests/env.sh start
     tests/env.sh run "$ENGINE" all
 
-/docker:
-  summary: Run all tests under Docker
-  environment:
-    ENGINE: docker
-
 /podman:
   summary: Run all tests under Podman
   environment:
@@ -58,3 +53,8 @@ execute:
   summary: Run all tests under Rootful Podman
   environment:
     ENGINE: rootful-podman
+
+/docker:
+  summary: Run all tests under Docker
+  environment:
+    ENGINE: docker
diff --git a/tests/env.sh b/tests/env.sh
index f6ed1d2..87143b4 100755
--- a/tests/env.sh
+++ b/tests/env.sh
@@ -53,7 +53,7 @@ COMMANDS
    run <engine> <test_script>
    run <engine> all
       Run a test script in the test env VM under the given engine. <engine> must
-      be one of 'docker', 'podman', 'rootful-podman', or 'all'.
+      be one of 'podman', 'rootful-podman', 'docker', or 'all'.
 
    ssh
       SSH into the test env VM for debugging.
@@ -268,9 +268,9 @@ start)
         __log_and_run podman save "$image" -o "$temp_dir/image.tar"
 
         __exec cp /home/fedora/images/image.tar image.tar
-        __exec sudo docker load -i image.tar
         __exec podman      load -i image.tar
         __exec sudo podman load -i image.tar
+        __exec sudo docker load -i image.tar
         __exec rm image.tar
 
         rm "$temp_dir/image.tar"
@@ -299,11 +299,11 @@ run)
     fi
 
     case "$2" in
-    docker|podman|rootful-podman)
+    podman|rootful-podman|docker)
         engines=( "$2" )
         ;;
     all)
-        engines=( docker podman rootful-podman )
+        engines=( podman rootful-podman docker )
         ;;
     *)
         __bad_usage
@@ -330,10 +330,6 @@ run)
             __big_log 33 'Running test %s under %s...' "$( __rel "$t" )" "$engine"
 
             case "$engine" in
-            docker)
-                engine_cmd=( sudo docker )
-                runtime_in_env=crun-vm
-                ;;
             podman)
                 engine_cmd=( podman )
                 runtime_in_env=/home/fedora/target/debug/crun-vm
@@ -342,6 +338,10 @@ run)
                 engine_cmd=( sudo podman )
                 runtime_in_env=/home/fedora/target/debug/crun-vm
                 ;;
+            docker)
+                engine_cmd=( sudo docker )
+                runtime_in_env=crun-vm
+                ;;
             esac
 
             # generate random label for containers created by test script