diff --git a/test/units/TEST-13-NSPAWN.machinectl.sh b/test/units/TEST-13-NSPAWN.machinectl.sh
index c27207bcc7..462cc6a8c3 100755
--- a/test/units/TEST-13-NSPAWN.machinectl.sh
+++ b/test/units/TEST-13-NSPAWN.machinectl.sh
@@ -132,6 +132,9 @@ machinectl show-image clone1
 machinectl rename clone1 clone2
 (! machinectl show-image clone1)
 machinectl show-image clone2
+# `machinectl read-only` uses chattr (ioctl(FS_IOC_SETFLAGS)) when the container is backed by a directory,
+# and this operation might not be implemented on certain filesystems (i.e. tmpfs on older kernels), so check
+# if we have chattr support before running following tests
 if lsattr -d /var/lib/machines >/dev/null; then
     [[ "$(machinectl show-image --property=ReadOnly --value clone2)" == no ]]
     machinectl read-only clone2 yes
diff --git a/test/units/TEST-65-ANALYZE.sh b/test/units/TEST-65-ANALYZE.sh
index 5f650ade05..18f5c4d804 100755
--- a/test/units/TEST-65-ANALYZE.sh
+++ b/test/units/TEST-65-ANALYZE.sh
@@ -303,7 +303,9 @@ systemd-analyze security --offline=true /tmp/testfile.service
 systemd-analyze security --offline=true /tmp/testfile.service | grep -q -F "/dev/sda"
 
 # Make sure that running generators under systemd-analyze verify works.
-systemd-analyze verify --generators /tmp/testfile.service
+# Note: sd-analyze spawns generators in a sandbox which makes gcov unhapy, so temporarily override
+#       $GCOV_PREFIX to make it skip generating any coverage reports
+GCOV_PREFIX=/tmp systemd-analyze verify --generators /tmp/testfile.service
 
 rm /tmp/testfile.service