diff --git a/test/TEST-41-ONESHOT-RESTART/blacklist-ubuntu-ci b/test/TEST-41-ONESHOT-RESTART/blacklist-ubuntu-ci
deleted file mode 100644
index 22b34bbb0c..0000000000
--- a/test/TEST-41-ONESHOT-RESTART/blacklist-ubuntu-ci
+++ /dev/null
@@ -1,4 +0,0 @@
-This appears to be failing on Ubuntu CI due to short sleep duration
-waiting for the service-restarts to complete, but doubling the
-sleep from 5 to 10 seconds didn't appear to help, so let's blacklist
-this on Ubuntu CI while debugging the test failure.
diff --git a/test/TEST-41-ONESHOT-RESTART/testsuite.sh b/test/TEST-41-ONESHOT-RESTART/testsuite.sh
index f7423dbf9a..4465614ff3 100755
--- a/test/TEST-41-ONESHOT-RESTART/testsuite.sh
+++ b/test/TEST-41-ONESHOT-RESTART/testsuite.sh
@@ -2,14 +2,19 @@
 set -ex
 set -o pipefail
 
+# wait this many secs for each test service to succeed in what is being tested
+MAX_SECS=60
+
 systemd-analyze log-level debug
 systemd-analyze log-target console
 
-# These three commands should succeed.
+# test one: Restart=on-failure should restart the service
 ! systemd-run --unit=one -p Type=oneshot -p Restart=on-failure /bin/bash -c "exit 1"
 
-sleep 5
-
+for ((secs=0; secs<$MAX_SECS; secs++)); do
+  [[ "$(systemctl show one.service -p NRestarts --value)" -le 0 ]] || break
+  sleep 1
+done
 if [[ "$(systemctl show one.service -p NRestarts --value)" -le 0 ]]; then
   exit 1
 fi
@@ -18,10 +23,21 @@ TMP_FILE="/test-41-oneshot-restart-test"
 
 touch $TMP_FILE
 
-! systemd-run --unit=two -p StartLimitBurst=3 -p Type=oneshot -p Restart=on-failure -p ExecStart="/bin/bash -c \"printf a >>  $TMP_FILE\"" /bin/bash -c "exit 1"
+# test two: make sure StartLimitBurst correctly limits the number of restarts
+# and restarts execution of the unit from the first ExecStart=
+! systemd-run --unit=two -p StartLimitIntervalSec=120 -p StartLimitBurst=3 -p Type=oneshot -p Restart=on-failure -p ExecStart="/bin/bash -c \"printf a >>  $TMP_FILE\"" /bin/bash -c "exit 1"
 
+# wait for at least 3 restarts
+for ((secs=0; secs<$MAX_SECS; secs++)); do
+  [[ $(cat $TMP_FILE) != "aaa" ]] || break
+  sleep 1
+done
+if [[ $(cat $TMP_FILE) != "aaa" ]]; then
+  exit 1
+fi
+
+# wait for 5 more seconds to make sure there aren't excess restarts
 sleep 5
-
 if [[ $(cat $TMP_FILE) != "aaa" ]]; then
   exit 1
 fi