diff --git a/test/system/060-mount.bats b/test/system/060-mount.bats
index 4498e675fb..dd8aa3e97b 100644
--- a/test/system/060-mount.bats
+++ b/test/system/060-mount.bats
@@ -50,10 +50,6 @@ load helpers
     run_podman image mount $IMAGE
     mount_path="$output"
 
-    # Make sure that `mount -a` prints a table
-    run_podman image mount -a
-    is "$output" "$IMAGE .*$mount_path"
-
     test -d $mount_path
 
     # Image is custom-built and has a file containing the YMD tag. Check it.
@@ -66,16 +62,23 @@ load helpers
     run_podman image mount
     is "$output" "$IMAGE *$mount_path" "podman image mount with no args"
 
-    # Clean up: -f since we mounted it twice
+    # Clean up, and make sure nothing is mounted any more
     run_podman image umount -f $IMAGE
     is "$output" "$iid" "podman image umount: image ID of what was umounted"
 
     run_podman image umount $IMAGE
     is "$output" "" "podman image umount: does not re-umount"
 
-    run_podman 125 image umount no-such-container
-    is "$output" "Error: no-such-container: image not known" \
-       "error message from image umount no-such-container"
+    run_podman 125 image umount no-such-image
+    is "$output" "Error: no-such-image: image not known" \
+       "error message from image umount no-such-image"
+
+    # Tests for mount -a. This may mount more than one image! (E.g. systemd)
+    run_podman image mount -a
+    is "$output" "$IMAGE .*$mount_path"
+
+    run_podman image umount -a
+    assert "$output" =~ "$iid" "Test image is unmounted"
 
     run_podman image mount
     is "$output" "" "podman image mount, no args, after umount"
diff --git a/test/system/120-load.bats b/test/system/120-load.bats
index 35a6eae421..904b5da49d 100644
--- a/test/system/120-load.bats
+++ b/test/system/120-load.bats
@@ -63,16 +63,6 @@ verify_iid_and_name() {
     run_podman images $fqin --format '{{.Repository}}:{{.Tag}}'
     is "${lines[0]}" "$fqin" "image preserves name across save/load"
 
-    # Load with a new tag
-    local new_name=x1$(random_string 14 | tr A-Z a-z)
-    local new_tag=t1$(random_string 6 | tr A-Z a-z)
-    run_podman rmi $fqin
-
-    run_podman load -i $archive
-    run_podman images --format '{{.Repository}}:{{.Tag}}' --sort tag
-    is "${lines[0]}" "$IMAGE"     "image is preserved"
-    is "${lines[1]}" "$fqin"      "image is reloaded with old fqin"
-
     # Clean up
     run_podman rmi $fqin
 }