diff --git a/test/system/020-tag.bats b/test/system/020-tag.bats
index 226523aa31..c776ff53bc 100644
--- a/test/system/020-tag.bats
+++ b/test/system/020-tag.bats
@@ -13,30 +13,34 @@ function _tag_and_check() {
     run_podman 1 image exists $check_as
 }
 
+# bats test_tags=ci:parallel
 @test "podman tag/untag" {
+    registry="bogusregistry.nxdomain"
+    imgname=i-$(safename)
+
     # Test a fully-qualified image reference.
-    _tag_and_check registry.com/image:latest registry.com/image:latest
+    _tag_and_check "$registry/$imgname:latest" "$registry/$imgname:latest"
 
     # Test a reference without tag and make sure ":latest" is appended.
-    _tag_and_check registry.com/image registry.com/image:latest
+    _tag_and_check "$registry/$imgname" "$registry/$imgname:latest"
 
     # Test a tagged short image and make sure "localhost/" is prepended.
-    _tag_and_check image:latest localhost/image:latest
+    _tag_and_check "$imgname:latest" "localhost/$imgname:latest"
 
     # Test a short image without tag and make sure "localhost/" is
     # prepended and ":latest" is appended.
-    _tag_and_check image localhost/image:latest
+    _tag_and_check "$imgname" "localhost/$imgname:latest"
 
     # The order is intentionally wrong here to check the sorting
     # /~https://github.com/containers/podman/issues/23803
-    local image1="registry.com/image:1"
+    local image1="$registry/$imgname-x:1"
     run_podman tag $IMAGE $image1
-    local image3="registry.com/image:3"
+    local image3="$registry/$imgname-x:3"
     run_podman tag $IMAGE $image3
-    local image2="registry.com/image:2"
+    local image2="$registry/$imgname-x:2"
     run_podman tag $IMAGE $image2
 
-    local imageA="registry.com/aaa:a"
+    local imageA="$registry/$imgname-a:a"
     run_podman tag $IMAGE $imageA
 
     local nl="
@@ -47,17 +51,24 @@ function _tag_and_check() {
     run_podman untag $IMAGE $imageA $image1 $image2 $image3
 
     # Test error case.
-    run_podman 125 untag $IMAGE registry.com/foo:bar
-    is "$output" "Error: registry.com/foo:bar: tag not known"
+    run_podman 125 untag $IMAGE "$registry/foo:bar"
+    is "$output" "Error: $registry/foo:bar: tag not known"
 }
 
+# CANNOT BE PARALLELIZED: temporarily removes $IMAGE
 @test "podman untag all" {
     # First get the image ID
     run_podman inspect --format '{{.ID}}' $IMAGE
     iid=$output
 
+    registry="bogusregistry.nxdomain"
+    imgname=i-$(safename)
+
     # Add a couple of tags
-    run_podman tag $IMAGE registry.com/1:latest registry.com/2:latest registry.com/3:latest
+    run_podman tag $IMAGE \
+               "$registry/$imgname-1:latest" \
+               "$registry/$imgname-2:latest" \
+               "$registry/$imgname-3:latest"
 
     # Untag with arguments to for all tags to be removed
     run_podman untag $iid
@@ -66,6 +77,8 @@ function _tag_and_check() {
     run_podman image inspect $iid --format "{{.RepoTags}}"
     is "$output" "\[\]" "untag by ID leaves empty set of tags"
 
+    run_podman 1 image exists $IMAGE
+
     # Restore image
     run_podman tag $iid $IMAGE
 }