diff --git a/tests/integration/events.bats b/tests/integration/events.bats
index 50c577e80..f51337598 100644
--- a/tests/integration/events.bats
+++ b/tests/integration/events.bats
@@ -112,11 +112,11 @@ function teardown() {
   [ "$status" -eq 0 ]
 }
 
-@test "events oom " {
+@test "events oom" {
   # XXX: currently cgroups require root containers.
-  requires root
+  requires root cgroups_swap
   init_cgroup_paths
-  
+
   # we need the container to hit OOM, so disable swap
   # ("swap" here is actually memory+swap)
   DATA=$(cat <<EOF
diff --git a/tests/integration/helpers.bash b/tests/integration/helpers.bash
index 98eb36f0b..ad43acb8d 100644
--- a/tests/integration/helpers.bash
+++ b/tests/integration/helpers.bash
@@ -266,6 +266,12 @@ function requires() {
 				skip_me=1
 			fi
 			;;
+		cgroups_swap)
+			init_cgroup_paths
+			if [ $CGROUP_UNIFIED = "no" -a ! -e "${CGROUP_MEMORY_BASE_PATH}/memory.memsw.limit_in_bytes" ]; then
+				skip_me=1
+			fi
+			;;
 		cgroups_v1)
 			init_cgroup_paths
 			if [ "$CGROUP_UNIFIED" != "no" ]; then
diff --git a/tests/integration/update.bats b/tests/integration/update.bats
index 4c1585e1d..08736e428 100644
--- a/tests/integration/update.bats
+++ b/tests/integration/update.bats
@@ -69,7 +69,10 @@ EOF
         MEM_SWAP="memory.memsw.limit_in_bytes"
         SD_MEM_SWAP="unsupported"
         SYSTEM_MEM=$(cat "${CGROUP_MEMORY_BASE_PATH}/${MEM_LIMIT}")
-        SYSTEM_MEM_SWAP=$(cat "${CGROUP_MEMORY_BASE_PATH}/$MEM_SWAP")
+        HAVE_SWAP="no"
+        if [ -f "${CGROUP_MEMORY_BASE_PATH}/${MEM_SWAP}" ]; then
+            HAVE_SWAP="yes"
+        fi
         ;;
     yes)
         MEM_LIMIT="memory.max"
@@ -79,8 +82,7 @@ EOF
         MEM_SWAP="memory.swap.max"
         SD_MEM_SWAP="MemorySwapMax"
         SYSTEM_MEM="max"
-        SYSTEM_MEM_SWAP="max"
-        CGROUP_MEMORY=$CGROUP_PATH
+        HAVE_SWAP="yes"
         ;;
     esac
     SD_UNLIMITED="infinity"
@@ -126,11 +128,11 @@ EOF
     check_systemd_value "$SD_MEM_RESERVE" 33554432
 
     # Run swap memory tests if swap is available
-    if [ -f "$CGROUP_MEMORY/$MEM_SWAP" ]; then
+    if [ "$HAVE_SWAP" = "yes" ]; then
         # try to remove memory swap limit
         runc update test_update --memory-swap -1
         [ "$status" -eq 0 ]
-        check_cgroup_value "$MEM_SWAP" $SYSTEM_MEM_SWAP
+        check_cgroup_value "$MEM_SWAP" $SYSTEM_MEM
         check_systemd_value "$SD_MEM_SWAP" $SD_UNLIMITED
 
         # update memory swap
@@ -158,7 +160,7 @@ EOF
     check_systemd_value $SD_MEM_LIMIT $SD_UNLIMITED
 
     # check swap memory limited is gone
-    if [ -f "$CGROUP_MEMORY/$MEM_SWAP" ]; then
+    if [ "$HAVE_SWAP" = "yes" ]; then
         check_cgroup_value $MEM_SWAP $SYSTEM_MEM
         check_systemd_value "$SD_MEM_SWAP" $SD_UNLIMITED
     fi