diff --git a/units/hwclock-save.service b/units/hwclock-save.service
index 11ad0eba2b..dedee767a2 100644
--- a/units/hwclock-save.service
+++ b/units/hwclock-save.service
@@ -8,7 +8,9 @@
 [Unit]
 Description=Update RTC With System Clock
 DefaultDependencies=no
-Before=poweroff.service reboot.service halt.service
+After=hwclock-load.service
+Before=shutdown.target
+Conflicts=hwclock-load.service
 
 [Service]
 Type=oneshot
diff --git a/units/systemd-random-seed-save.service.in b/units/systemd-random-seed-save.service.in
index 6539bdceff..9a074cf3fe 100644
--- a/units/systemd-random-seed-save.service.in
+++ b/units/systemd-random-seed-save.service.in
@@ -8,7 +8,8 @@
 [Unit]
 Description=Save Random Seed
 DefaultDependencies=no
-Before=poweroff.service reboot.service halt.service
+After=systemd-random-seed-load.service
+Before=shutdown.target
 Conflicts=systemd-random-seed-load.service
 
 [Service]