diff --git a/src/generator.rs b/src/generator.rs
index abea890e..2aa8a13a 100644
--- a/src/generator.rs
+++ b/src/generator.rs
@@ -217,6 +217,16 @@ fn handle_zram_swap(output_directory: &Path, device: &Device) -> Result<()> {
 
     handle_zram_bindings(output_directory, device, "dev-%i.swap")?;
 
+    let shutdown_conflicts = if device.writeback_dev.is_some() {
+        // We need to shut down the zram device to disconnect the writeback device.
+        // Once https://github.com/systemd/systemd/issues/35303 is resolved, we
+        // may revisit this and rely on the systemd to pull down the device stack
+        // if appropriate.
+        "Conflicts=shutdown.target\n"
+    } else {
+        ""
+    };
+
     /* dev-zramX.swap */
     write_contents(
         output_directory,
@@ -226,9 +236,13 @@ fn handle_zram_swap(output_directory: &Path, device: &Device) -> Result<()> {
 [Unit]
 Description=Compressed Swap on /dev/{zram_device}
 Documentation=man:zram-generator(8) man:zram-generator.conf(5)
+
+DefaultDependencies=no
+
 Requires=systemd-zram-setup@{zram_device}.service
 After=systemd-zram-setup@{zram_device}.service
-
+Before=swap.target
+{shutdown_conflicts}
 [Swap]
 What=/dev/{zram_device}
 Priority={swap_priority}
@@ -237,6 +251,7 @@ Options={options}
             zram_device = device.name,
             swap_priority = device.swap_priority,
             options = device.options.replace('%', "%%"),
+            shutdown_conflicts = shutdown_conflicts,
         ),
     )?;
 
diff --git a/tests/01-basic/run.expected/units/dev-zram0.swap b/tests/01-basic/run.expected/units/dev-zram0.swap
index f379af15..0159a88c 100644
--- a/tests/01-basic/run.expected/units/dev-zram0.swap
+++ b/tests/01-basic/run.expected/units/dev-zram0.swap
@@ -3,8 +3,12 @@
 [Unit]
 Description=Compressed Swap on /dev/zram0
 Documentation=man:zram-generator(8) man:zram-generator.conf(5)
+
+DefaultDependencies=no
+
 Requires=systemd-zram-setup@zram0.service
 After=systemd-zram-setup@zram0.service
+Before=swap.target
 
 [Swap]
 What=/dev/zram0
diff --git a/tests/02-zstd/run.expected/units/dev-zram0.swap b/tests/02-zstd/run.expected/units/dev-zram0.swap
index f379af15..0159a88c 100644
--- a/tests/02-zstd/run.expected/units/dev-zram0.swap
+++ b/tests/02-zstd/run.expected/units/dev-zram0.swap
@@ -3,8 +3,12 @@
 [Unit]
 Description=Compressed Swap on /dev/zram0
 Documentation=man:zram-generator(8) man:zram-generator.conf(5)
+
+DefaultDependencies=no
+
 Requires=systemd-zram-setup@zram0.service
 After=systemd-zram-setup@zram0.service
+Before=swap.target
 
 [Swap]
 What=/dev/zram0
diff --git a/tests/04-dropins/run.expected/units/dev-zram0.swap b/tests/04-dropins/run.expected/units/dev-zram0.swap
index f379af15..0159a88c 100644
--- a/tests/04-dropins/run.expected/units/dev-zram0.swap
+++ b/tests/04-dropins/run.expected/units/dev-zram0.swap
@@ -3,8 +3,12 @@
 [Unit]
 Description=Compressed Swap on /dev/zram0
 Documentation=man:zram-generator(8) man:zram-generator.conf(5)
+
+DefaultDependencies=no
+
 Requires=systemd-zram-setup@zram0.service
 After=systemd-zram-setup@zram0.service
+Before=swap.target
 
 [Swap]
 What=/dev/zram0
diff --git a/tests/04-dropins/run.expected/units/dev-zram2.swap b/tests/04-dropins/run.expected/units/dev-zram2.swap
index 1d794385..2a35ad48 100644
--- a/tests/04-dropins/run.expected/units/dev-zram2.swap
+++ b/tests/04-dropins/run.expected/units/dev-zram2.swap
@@ -3,8 +3,12 @@
 [Unit]
 Description=Compressed Swap on /dev/zram2
 Documentation=man:zram-generator(8) man:zram-generator.conf(5)
+
+DefaultDependencies=no
+
 Requires=systemd-zram-setup@zram2.service
 After=systemd-zram-setup@zram2.service
+Before=swap.target
 
 [Swap]
 What=/dev/zram2
diff --git a/tests/06-kernel-enabled/run.expected/units/dev-zram0.swap b/tests/06-kernel-enabled/run.expected/units/dev-zram0.swap
index f379af15..0159a88c 100644
--- a/tests/06-kernel-enabled/run.expected/units/dev-zram0.swap
+++ b/tests/06-kernel-enabled/run.expected/units/dev-zram0.swap
@@ -3,8 +3,12 @@
 [Unit]
 Description=Compressed Swap on /dev/zram0
 Documentation=man:zram-generator(8) man:zram-generator.conf(5)
+
+DefaultDependencies=no
+
 Requires=systemd-zram-setup@zram0.service
 After=systemd-zram-setup@zram0.service
+Before=swap.target
 
 [Swap]
 What=/dev/zram0
diff --git a/tests/09-zram-size/run.expected/units/dev-zram0.swap b/tests/09-zram-size/run.expected/units/dev-zram0.swap
index f379af15..0159a88c 100644
--- a/tests/09-zram-size/run.expected/units/dev-zram0.swap
+++ b/tests/09-zram-size/run.expected/units/dev-zram0.swap
@@ -3,8 +3,12 @@
 [Unit]
 Description=Compressed Swap on /dev/zram0
 Documentation=man:zram-generator(8) man:zram-generator.conf(5)
+
+DefaultDependencies=no
+
 Requires=systemd-zram-setup@zram0.service
 After=systemd-zram-setup@zram0.service
+Before=swap.target
 
 [Swap]
 What=/dev/zram0
diff --git a/tests/10-example/run.expected/units/dev-zram0.swap b/tests/10-example/run.expected/units/dev-zram0.swap
index 92d411c1..6f2b3d8b 100644
--- a/tests/10-example/run.expected/units/dev-zram0.swap
+++ b/tests/10-example/run.expected/units/dev-zram0.swap
@@ -3,8 +3,13 @@
 [Unit]
 Description=Compressed Swap on /dev/zram0
 Documentation=man:zram-generator(8) man:zram-generator.conf(5)
+
+DefaultDependencies=no
+
 Requires=systemd-zram-setup@zram0.service
 After=systemd-zram-setup@zram0.service
+Before=swap.target
+Conflicts=shutdown.target
 
 [Swap]
 What=/dev/zram0
diff --git a/tests/11-obsolete/run.expected/units/dev-zram0.swap b/tests/11-obsolete/run.expected/units/dev-zram0.swap
index f379af15..0159a88c 100644
--- a/tests/11-obsolete/run.expected/units/dev-zram0.swap
+++ b/tests/11-obsolete/run.expected/units/dev-zram0.swap
@@ -3,8 +3,12 @@
 [Unit]
 Description=Compressed Swap on /dev/zram0
 Documentation=man:zram-generator(8) man:zram-generator.conf(5)
+
+DefaultDependencies=no
+
 Requires=systemd-zram-setup@zram0.service
 After=systemd-zram-setup@zram0.service
+Before=swap.target
 
 [Swap]
 What=/dev/zram0
diff --git a/tests/11-obsolete/run.expected/units/dev-zram1.swap b/tests/11-obsolete/run.expected/units/dev-zram1.swap
index 39d74be1..95196816 100644
--- a/tests/11-obsolete/run.expected/units/dev-zram1.swap
+++ b/tests/11-obsolete/run.expected/units/dev-zram1.swap
@@ -3,8 +3,12 @@
 [Unit]
 Description=Compressed Swap on /dev/zram1
 Documentation=man:zram-generator(8) man:zram-generator.conf(5)
+
+DefaultDependencies=no
+
 Requires=systemd-zram-setup@zram1.service
 After=systemd-zram-setup@zram1.service
+Before=swap.target
 
 [Swap]
 What=/dev/zram1