diff --git a/test/system/500-networking.bats b/test/system/500-networking.bats
index b37c2fda25f9..9bfaf05aa44c 100644
--- a/test/system/500-networking.bats
+++ b/test/system/500-networking.bats
@@ -1095,4 +1095,24 @@ function wait_for_restart_count() {
     run_podman network rm $netname
 }
 
+# 2024-07-23 moved from 505 pasta tests because it can't run in parallel
+# CANNOT BE PARALLELIZED
+@test "Podman unshare --rootless-netns with Pasta" {
+    skip_if_remote "unshare is local-only"
+    skip_if_not_rootless "pasta networking only available in rootless mode"
+    skip_if_no_pasta "pasta not found; this test requires pasta"
+
+    pasta_iface=$(default_ifname 4)
+    assert "$pasta_iface" != "" "pasta_iface is set"
+
+    # First let's force a setup error by making pasta be "false".
+    ln -s /usr/bin/false $PODMAN_TMPDIR/pasta
+    CONTAINERS_HELPER_BINARY_DIR="$PODMAN_TMPDIR" run_podman 125 unshare --rootless-netns ip addr
+    assert "$output" =~ "pasta failed with exit code 1"
+
+    # Now this should recover from the previous error and setup the netns correctly.
+    run_podman unshare --rootless-netns ip addr
+    is "$output" ".*${pasta_iface}.*"
+}
+
 # vim: filetype=sh
diff --git a/test/system/505-networking-pasta.bats b/test/system/505-networking-pasta.bats
index 9f0af92c34c7..f32e3e427d18 100644
--- a/test/system/505-networking-pasta.bats
+++ b/test/system/505-networking-pasta.bats
@@ -10,6 +10,9 @@
 load helpers
 load helpers.network
 
+# All tests in this file must be able to run in parallel
+# bats file_tags=ci:parallel
+
 function setup() {
     basic_setup
     skip_if_not_rootless "pasta networking only available in rootless mode"
@@ -156,7 +159,7 @@ function pasta_test_do() {
         local seq="$(echo ${port} | tr '-' ' ')"
         local xseq="$(echo ${xport} | tr '-' ' ')"
     else
-        local port=$(random_free_port "" ${address} ${proto})
+        local port=$(random_free_port "" ${addr} ${proto})
         local xport="$((port + delta))"
         local seq="${port} ${port}"
         local xseq="${xport} ${xport}"
@@ -336,7 +339,7 @@ function pasta_test_do() {
 @test "podman puts pasta IP in /etc/hosts" {
     skip_if_no_ipv4 "IPv4 not routable on the host"
 
-    pname="p$(random_string 30)"
+    pname="p-$(safename)"
     ip="$(default_addr 4)"
 
     run_podman pod create --net=pasta --name "${pname}"
@@ -345,7 +348,6 @@ function pasta_test_do() {
     assert "$(echo ${output} | cut -f1 -d' ')" = "${ip}" "Correct /etc/hosts entry missing"
 
     run_podman pod rm "${pname}"
-    run_podman rmi $(pause_image)
 }
 
 ### Routes #####################################################################
@@ -766,8 +768,21 @@ function pasta_test_do() {
     local pidfile="${PODMAN_TMPDIR}/pasta.pid"
 
     run_podman run --rm "--net=pasta:--pid,${pidfile}" $IMAGE true
-    sleep 1
-    ! ps -p $(cat "${pidfile}") && rm "${pidfile}"
+
+    # Allow time for process to vanish, in case there's high load
+    local pid=$(< $pidfile)
+    local timeout=5
+    while [[ $timeout -gt 0 ]]; do
+        if ! ps -p $pid; then
+            return
+        fi
+
+        # Still alive. Wait and retry
+        sleep 1
+        timeout=$((timeout - 1))
+    done
+
+    die "Timed out waiting for pid $pid to terminate"
 }
 
 ### Options ####################################################################
@@ -801,24 +816,6 @@ EOF
     assert "$output" =~ "$mac2" "mac address from cli is set on custom interface"
 }
 
-### Rootless unshare testing
-
-@test "Podman unshare --rootless-netns with Pasta" {
-    skip_if_remote "unshare is local-only"
-
-    pasta_iface=$(default_ifname 4)
-    assert "$pasta_iface" != "" "pasta_iface is set"
-
-    # First let's force a setup error by making pasta be "false".
-    ln -s /usr/bin/false $PODMAN_TMPDIR/pasta
-    CONTAINERS_HELPER_BINARY_DIR="$PODMAN_TMPDIR" run_podman 125 unshare --rootless-netns ip addr
-    assert "$output" =~ "pasta failed with exit code 1"
-
-    # Now this should recover from the previous error and setup the netns correctly.
-    run_podman unshare --rootless-netns ip addr
-    is "$output" ".*${pasta_iface}.*"
-}
-
 # https://github.com/containers/podman/issues/22653
 @test "pasta/bridge and host.containers.internal" {
     skip_if_no_ipv4 "IPv4 not routable on the host"