diff --git a/units/syslog.target b/units/syslog.target
index 8b1626ed55..825b26e7bf 100644
--- a/units/syslog.target
+++ b/units/syslog.target
@@ -12,3 +12,8 @@
 
 [Unit]
 Description=Syslog
+
+# Avoid that we conflict with shutdown.target, so that we can stay
+# until the very end and do not cancel shutdown.target if we should
+# hapen to be activated very late.
+DefaultDependencies=no
diff --git a/units/systemd-update-utmp-runlevel.service.in b/units/systemd-update-utmp-runlevel.service.in
index 865a1535de..614c759a63 100644
--- a/units/systemd-update-utmp-runlevel.service.in
+++ b/units/systemd-update-utmp-runlevel.service.in
@@ -8,7 +8,6 @@
 [Unit]
 Description=Notify Audit System and Update UTMP about System Runlevel Changes
 DefaultDependencies=no
-Wants=local-fs.target sysinit.target
 After=local-fs.target sysinit.target auditd.service runlevel1.target runlevel2.target runlevel3.target runlevel4.target runlevel5.target systemd-tmpfiles-setup.service
 Before=poweroff.service reboot.service halt.service
 
diff --git a/units/systemd-update-utmp-shutdown.service.in b/units/systemd-update-utmp-shutdown.service.in
index c30d86d24c..e7c3c04a00 100644
--- a/units/systemd-update-utmp-shutdown.service.in
+++ b/units/systemd-update-utmp-shutdown.service.in
@@ -8,7 +8,6 @@
 [Unit]
 Description=Notify Audit System and Update UTMP about System Shutdown
 DefaultDependencies=no
-Wants=local-fs.target sysinit.target
 After=local-fs.target sysinit.target auditd.service systemd-update-utmp-runlevel.service
 Before=poweroff.service reboot.service halt.service