diff --git a/test/system/015-help.bats b/test/system/015-help.bats
index 36bda467cf..75fed8fb56 100644
--- a/test/system/015-help.bats
+++ b/test/system/015-help.bats
@@ -196,6 +196,7 @@ function check_help() {
 }
 
 
+# bats test_tags=ci:parallel
 @test "podman help - basic tests" {
     skip_if_remote
 
diff --git a/test/system/065-cp.bats b/test/system/065-cp.bats
index 33dc8dd10f..dd2f9c0a5c 100644
--- a/test/system/065-cp.bats
+++ b/test/system/065-cp.bats
@@ -7,6 +7,9 @@
 
 load helpers
 
+# All tests here can be run in parallel
+# bats file_tags=ci:parallel
+
 @test "podman cp file from host to container" {
     srcdir=$PODMAN_TMPDIR/cp-test-file-host-to-ctr
     mkdir -p $srcdir
diff --git a/test/system/075-exec.bats b/test/system/075-exec.bats
index 3aed8ff2c0..9faa6a7e2b 100644
--- a/test/system/075-exec.bats
+++ b/test/system/075-exec.bats
@@ -5,7 +5,7 @@
 
 load helpers
 
-# bats test_tags=distro-integration
+# bats test_tags=distro-integration, ci:parallel
 @test "podman exec - basic test" {
     rand_filename=$(random_string 20)
     rand_content=$(random_string 50)
@@ -47,7 +47,7 @@ load helpers
     run_podman rm $cid
 }
 
-# bats test_tags=distro-integration
+# bats test_tags=distro-integration, ci:parallel
 @test "podman exec - leak check" {
     skip_if_remote "test is meaningless over remote"
 
@@ -69,6 +69,7 @@ load helpers
 
 # Issue #4785 - piping to exec statement - fixed in #4818
 # Issue #5046 - piping to exec truncates results (actually a conmon issue)
+# bats test_tags=ci:parallel
 @test "podman exec - cat from stdin" {
     run_podman run -d $IMAGE top
     cid="$output"
@@ -95,6 +96,7 @@ load helpers
 }
 
 # #6829 : add username to /etc/passwd inside container if --userns=keep-id
+# bats test_tags=ci:parallel
 @test "podman exec - with keep-id" {
     skip_if_not_rootless "--userns=keep-id only works in rootless mode"
     # Multiple --userns options confirm command-line override (last one wins)
@@ -109,6 +111,7 @@ load helpers
 }
 
 # #11496: podman-remote loses output
+# bats test_tags=ci:parallel
 @test "podman exec/run - missing output" {
     local bigfile=${PODMAN_TMPDIR}/bigfile
     local newfile=${PODMAN_TMPDIR}/newfile
@@ -136,6 +139,7 @@ load helpers
     run_podman rm -t 0 -f $cid
 }
 
+# bats test_tags=ci:parallel
 @test "podman run umask" {
     umask="0724"
     run_podman run --rm -q $IMAGE grep Umask /proc/self/status
@@ -162,6 +166,7 @@ load helpers
     run_podman rm -f -t0 $cid
 }
 
+# bats test_tags=ci:parallel
 @test "podman exec --tty" {
     # Run all tests, report failures at end
     defer-assertion-failures
@@ -173,7 +178,8 @@ load helpers
             if [[ -n "$run_term_env" ]]; then
                 run_opt_env="--env=TERM=$run_term_env"
             fi
-            run_podman run -d $run_opt_t $run_opt_env --name test $IMAGE top
+            cname="c-${run_opt_t}-${run_term_env}-$(safename)"
+            run_podman run -d $run_opt_t $run_opt_env --name $cname $IMAGE top
 
             # Inner loops: different variations on EXEC
             for exec_opt_t in "" "-t"; do
@@ -196,16 +202,17 @@ load helpers
                     fi
 
                     local desc="run $run_opt_t $run_opt_env, exec $exec_opt_t $exec_opt_env"
-                    TERM=exec-term run_podman exec $exec_opt_t $exec_opt_env test sh -c 'echo -n $TERM'
+                    TERM=exec-term run_podman exec $exec_opt_t $exec_opt_env $cname sh -c 'echo -n $TERM'
                     assert "$output" = "$expected" "$desc"
                 done
             done
 
-            run_podman rm -f -t0 test
+            run_podman rm -f -t0 $cname
         done
     done
 }
 
+# bats test_tags=ci:parallel
 @test "podman exec - does not leak session IDs on invalid command" {
     run_podman run -d $IMAGE top
     cid="$output"
@@ -222,6 +229,7 @@ load helpers
 }
 
 # 'exec --preserve-fd' passes a list of additional file descriptors into the container
+# bats test_tags=ci:parallel
 @test "podman exec --preserve-fd" {
     skip_if_remote "preserve-fd is meaningless over remote"
 
diff --git a/test/system/271-tcp-cors-server.bats b/test/system/271-tcp-cors-server.bats
index 834beecd61..83816b10c0 100644
--- a/test/system/271-tcp-cors-server.bats
+++ b/test/system/271-tcp-cors-server.bats
@@ -13,6 +13,7 @@ SERVICE_TCP_HOST="localhost"
 SERVICE_FILE="$UNIT_DIR/$SERVICE_NAME.service"
 SOCKET_FILE="$UNIT_DIR/$SERVICE_NAME.socket"
 
+# bats test_tags=ci:parallel
 @test "podman system service - tcp CORS" {
     skip_if_remote "system service tests are meaningless over remote"
     PORT=$(random_free_port 63000-64999)
@@ -30,6 +31,7 @@ SOCKET_FILE="$UNIT_DIR/$SERVICE_NAME.socket"
            "podman warns about server on TCP"
 }
 
+# bats test_tags=ci:parallel
 @test "podman system service - tcp without CORS" {
     skip_if_remote "system service tests are meaningless over remote"
     PORT=$(random_free_port 63000-64999)
@@ -41,10 +43,15 @@ SOCKET_FILE="$UNIT_DIR/$SERVICE_NAME.socket"
     wait $podman_pid || true
 }
 
+# bats test_tags=ci:parallel
 @test "podman system service - CORS enabled in logs" {
     skip_if_remote "system service tests are meaningless over remote"
-    run_podman system service --log-level="debug" --cors="*" -t 1
+
+    PORT=$(random_free_port 63000-64999)
+    run_podman 0+w system service --log-level="debug" --cors="*" -t 1 tcp:$SERVICE_TCP_HOST:$PORT
     is "$output" ".*CORS Headers were set to ..\*...*" "debug log confirms CORS headers set"
+    assert "$output" =~ "level=warning msg=\"Using the Podman API service with TCP sockets is not recommended" \
+           "TCP socket warning"
 }
 
 # vim: filetype=sh
diff --git a/test/system/420-cgroups.bats b/test/system/420-cgroups.bats
index 62cb6aa4ee..084c9ae1c3 100644
--- a/test/system/420-cgroups.bats
+++ b/test/system/420-cgroups.bats
@@ -5,6 +5,7 @@
 
 load helpers
 
+# bats test_tags=ci:parallel
 @test "podman run, preserves initial --cgroup-manager" {
     skip_if_remote "podman-remote does not support --cgroup-manager"
 
@@ -37,7 +38,7 @@ load helpers
     run_podman rm myc
 }
 
-# bats test_tags=distro-integration
+# bats test_tags=distro-integration, ci:parallel
 @test "podman run --cgroups=disabled keeps the current cgroup" {
     skip_if_remote "podman-remote does not support --cgroups=disabled"
     skip_if_rootless_cgroupsv1
diff --git a/test/system/600-completion.bats b/test/system/600-completion.bats
index e719e5ad93..fe3da843d3 100644
--- a/test/system/600-completion.bats
+++ b/test/system/600-completion.bats
@@ -262,6 +262,7 @@ function _check_no_suggestions() {
 }
 
 
+# bats test_tags=ci:parallel
 @test "podman shell completion test" {
 
     random_container_name="c-$(safename)"
@@ -351,6 +352,7 @@ function _check_no_suggestions() {
     done
 }
 
+# bats test_tags=ci:parallel
 @test "podman shell completion for paths in container/image" {
     skip_if_remote "mounting via remote does not work"
     for cmd in create run; do
diff --git a/test/system/620-option-conflicts.bats b/test/system/620-option-conflicts.bats
index 1486c23ca5..f3889b3655 100644
--- a/test/system/620-option-conflicts.bats
+++ b/test/system/620-option-conflicts.bats
@@ -6,6 +6,7 @@
 load helpers
 
 
+# bats test_tags=ci:parallel
 @test "options that cannot be set together" {
     skip_if_remote "not much point testing remote, and container-cleanup fails anyway"