diff --git a/test/test-functions b/test/test-functions
index 5af7b8cd91..77da9259d7 100644
--- a/test/test-functions
+++ b/test/test-functions
@@ -1840,7 +1840,8 @@ save_journal() {
     # Show messages from the testsuite-XX.service or messages with priority "warning" and higher
     echo " --- $source_dir ---"
     "$JOURNALCTL" --no-pager --no-hostname -o short-monotonic -D "$source_dir" \
-        _SYSTEMD_UNIT="testsuite-${TESTID:?}.service" + PRIORITY=4 + PRIORITY=3 + PRIORITY=2 + PRIORITY=1 + PRIORITY=0
+        _SYSTEMD_UNIT="testsuite-${TESTID:?}.service" + SYSLOG_IDENTIFIER="testsuite-$TESTID.sh" + \
+        PRIORITY=4 + PRIORITY=3 + PRIORITY=2 + PRIORITY=1 + PRIORITY=0
 
     if get_bool "$save"; then
         # If we don't have systemd-journal-remote copy all journals from /var/log/journal/
diff --git a/test/units/testsuite-21.sh b/test/units/testsuite-21.sh
index 0b0dfc6c83..7b2013fb51 100755
--- a/test/units/testsuite-21.sh
+++ b/test/units/testsuite-21.sh
@@ -21,16 +21,32 @@ at_exit() {
     fi
 }
 
+add_suppression() {
+    local interface="${1:?}"
+    local suppression="${2:?}"
+
+    sed -i "\%\[$interface\]%a$suppression" /etc/dfuzzer.conf
+}
+
 trap at_exit EXIT
 
 systemctl log-level info
 
 # FIXME: systemd-run doesn't play well with daemon-reexec
 # See: https://github.com/systemd/systemd/issues/27204
-sed -i '/\[org.freedesktop.systemd1\]/aorg.freedesktop.systemd1.Manager:Reexecute FIXME' /etc/dfuzzer.conf
+add_suppression "org.freedesktop.systemd1" "org.freedesktop.systemd1.Manager:Reexecute FIXME"
 
-sed -i '/\[org.freedesktop.systemd1\]/aorg.freedesktop.systemd1.Manager:SoftReboot destructive' /etc/dfuzzer.conf
-sed -i '/\[org.freedesktop.login1\]/aSleep destructive' /etc/dfuzzer.conf
+add_suppression "org.freedesktop.systemd1" "org.freedesktop.systemd1.Manager:SoftReboot destructive"
+add_suppression "org.freedesktop.login1" "Sleep destructive"
+
+# Skip calling start and stop methods on unit objects, as doing that is not only time consuming, but it also
+# starts/stops units that interfere with the machine state. The actual code paths should be covered (to some
+# degree) by the respective method counterparts on the manager object.
+for method in Start Stop Restart ReloadOrRestart ReloadOrTryRestart Kill; do
+    add_suppression "org.freedesktop.systemd1" "org.freedesktop.systemd1.Unit:$method"
+done
+
+cat /etc/dfuzzer.conf
 
 # TODO
 #   * check for possibly newly introduced buses?