diff --git a/units/systemd-update-utmp-runlevel.service.in b/units/systemd-update-utmp-runlevel.service.in
index a288d6eb21..724e4a4c3a 100644
--- a/units/systemd-update-utmp-runlevel.service.in
+++ b/units/systemd-update-utmp-runlevel.service.in
@@ -8,9 +8,8 @@
 [Unit]
 Description=Notify Audit System and Update UTMP about System Runlevel Changes
 DefaultDependencies=no
+Before=poweroff.service reboot.service halt.service killall.service
 After=runlevel1.target runlevel2.target runlevel3.target runlevel4.target runlevel5.target auditd.service
-Conflicts=shutdown.target
-Before=shutdown.target
 
 [Service]
 Type=oneshot
diff --git a/units/systemd-update-utmp-shutdown.service.in b/units/systemd-update-utmp-shutdown.service.in
index e071285e3a..2042b71cb7 100644
--- a/units/systemd-update-utmp-shutdown.service.in
+++ b/units/systemd-update-utmp-shutdown.service.in
@@ -9,7 +9,7 @@
 Description=Notify Audit System and Update UTMP about System Shutdown
 DefaultDependencies=no
 Before=poweroff.service reboot.service halt.service killall.service
-Conflicts=systemd-update-utmp-runlevel.service
+After=systemd-update-utmp-runlevel.service
 
 [Service]
 Type=oneshot