diff --git a/units/container-getty@.service.m4.in b/units/container-getty@.service.m4.in
index 4b822f0e3b..3d287b9491 100644
--- a/units/container-getty@.service.m4.in
+++ b/units/container-getty@.service.m4.in
@@ -19,8 +19,8 @@ ConditionPathExists=/dev/pts/%I
 
 # IgnoreOnIsolate is an issue: when someone isolates rescue.target,
 # tradition expects that we shut down all but the main console.
-Conflicts=rescue.service
-Before=rescue.service
+Conflicts=rescue.service emergency.service
+Before=rescue.service emergency.service
 
 [Service]
 # The '-o' option value tells agetty to replace 'login' arguments with an
diff --git a/units/getty@.service.m4 b/units/getty@.service.m4
index ff1b3c3d87..c2665e3f6b 100644
--- a/units/getty@.service.m4
+++ b/units/getty@.service.m4
@@ -23,8 +23,8 @@ IgnoreOnIsolate=yes
 # IgnoreOnIsolate causes issues with sulogin, if someone isolates
 # rescue.target or starts rescue.service from multi-user.target or
 # graphical.target.
-Conflicts=rescue.service
-Before=rescue.service
+Conflicts=rescue.service emergency.service
+Before=rescue.service emergency.service
 
 # On systems without virtual consoles, don't start any getty. Note
 # that serial gettys are covered by serial-getty@.service, not this
diff --git a/units/serial-getty@.service.m4 b/units/serial-getty@.service.m4
index e56f47652c..d6da914454 100644
--- a/units/serial-getty@.service.m4
+++ b/units/serial-getty@.service.m4
@@ -24,8 +24,8 @@ IgnoreOnIsolate=yes
 # IgnoreOnIsolate causes issues with sulogin, if someone isolates
 # rescue.target or starts rescue.service from multi-user.target or
 # graphical.target.
-Conflicts=rescue.service
-Before=rescue.service
+Conflicts=rescue.service emergency.service
+Before=rescue.service emergency.service
 
 [Service]
 # The '-o' option value tells agetty to replace 'login' arguments with an
diff --git a/units/sysinit.target b/units/sysinit.target
index ec33503330..8d01cbdc1b 100644
--- a/units/sysinit.target
+++ b/units/sysinit.target
@@ -8,6 +8,13 @@
 [Unit]
 Description=System Initialization
 Documentation=man:systemd.special(7)
-Conflicts=emergency.service emergency.target
-Wants=local-fs.target swap.target
-After=local-fs.target swap.target emergency.service emergency.target
+Wants=swap.target local-fs.target
+After=swap.target local-fs.target
+
+# local-fs.target uses OnFailure="emergency.target" to start an emergency
+# shell.  In that case we also need to cancel everything that relies on
+# local-fs.target.  Flooding the screen with yellow [DEPEND] failures would
+# be unhelpful.  Therefore we break the chain here.  We use a Wants
+# dependency instead of Requires, and use a Conflict with emergency.target,
+# so that we are cancelled without actually failing any more units.
+Conflicts=emergency.target