diff --git a/src/core/unit.c b/src/core/unit.c
index ce0b197e6b..7964863470 100644
--- a/src/core/unit.c
+++ b/src/core/unit.c
@@ -1055,6 +1055,16 @@ int unit_add_exec_dependencies(Unit *u, ExecContext *c) {
         if (!MANAGER_IS_SYSTEM(u->manager))
                 return 0;
 
+        /* For the following three directory types we need write access, and /var/ is possibly on the root
+         * fs. Hence order after systemd-remount-fs.service, to ensure things are writable. */
+        if (!strv_isempty(c->directories[EXEC_DIRECTORY_STATE].paths) ||
+            !strv_isempty(c->directories[EXEC_DIRECTORY_CACHE].paths) ||
+            !strv_isempty(c->directories[EXEC_DIRECTORY_LOGS].paths)) {
+                r = unit_add_dependency_by_name(u, UNIT_AFTER, SPECIAL_REMOUNT_FS_SERVICE, true, UNIT_DEPENDENCY_FILE);
+                if (r < 0)
+                        return r;
+        }
+
         if (c->private_tmp) {
                 const char *p;
 
diff --git a/units/systemd-backlight@.service.in b/units/systemd-backlight@.service.in
index d3022856f2..6f7967fd00 100644
--- a/units/systemd-backlight@.service.in
+++ b/units/systemd-backlight@.service.in
@@ -12,7 +12,6 @@ Description=Load/Save Screen Backlight Brightness of %i
 Documentation=man:systemd-backlight@.service(8)
 DefaultDependencies=no
 Conflicts=shutdown.target
-After=systemd-remount-fs.service
 Before=sysinit.target shutdown.target
 
 [Service]
diff --git a/units/systemd-coredump@.service.in b/units/systemd-coredump@.service.in
index 951faa62a1..d1ece27074 100644
--- a/units/systemd-coredump@.service.in
+++ b/units/systemd-coredump@.service.in
@@ -12,7 +12,7 @@ Description=Process Core Dump
 Documentation=man:systemd-coredump(8)
 DefaultDependencies=no
 Conflicts=shutdown.target
-After=systemd-remount-fs.service systemd-journald.socket
+After=systemd-journald.socket
 Requires=systemd-journald.socket
 Before=shutdown.target
 
diff --git a/units/systemd-pstore.service.in b/units/systemd-pstore.service.in
index 89f34afe34..6e4827f03c 100644
--- a/units/systemd-pstore.service.in
+++ b/units/systemd-pstore.service.in
@@ -13,8 +13,8 @@ Documentation=man:systemd-pstore(8)
 ConditionDirectoryNotEmpty=/sys/fs/pstore
 ConditionVirtualization=!container
 DefaultDependencies=no
-Wants=systemd-remount-fs.service
-After=systemd-remount-fs.service
+Conflicts=shutdown.target
+Before=sysinit.target shutdown.target
 
 [Service]
 Type=oneshot
@@ -23,4 +23,4 @@ RemainAfterExit=yes
 StateDirectory=systemd/pstore
 
 [Install]
-WantedBy=systemd-remount-fs.service
+WantedBy=sysinit.target
diff --git a/units/systemd-rfkill.service.in b/units/systemd-rfkill.service.in
index 3abb958310..af2042f1e5 100644
--- a/units/systemd-rfkill.service.in
+++ b/units/systemd-rfkill.service.in
@@ -13,7 +13,7 @@ Documentation=man:systemd-rfkill.service(8)
 DefaultDependencies=no
 BindsTo=sys-devices-virtual-misc-rfkill.device
 Conflicts=shutdown.target
-After=sys-devices-virtual-misc-rfkill.device systemd-remount-fs.service
+After=sys-devices-virtual-misc-rfkill.device
 Before=shutdown.target
 
 [Service]
diff --git a/units/systemd-timesyncd.service.in b/units/systemd-timesyncd.service.in
index f0486a70ab..92ee94582c 100644
--- a/units/systemd-timesyncd.service.in
+++ b/units/systemd-timesyncd.service.in
@@ -13,7 +13,7 @@ Documentation=man:systemd-timesyncd.service(8)
 ConditionCapability=CAP_SYS_TIME
 ConditionVirtualization=!container
 DefaultDependencies=no
-After=systemd-remount-fs.service systemd-sysusers.service
+After=systemd-sysusers.service
 Before=time-set.target sysinit.target shutdown.target
 Conflicts=shutdown.target
 Wants=time-set.target time-sync.target