diff --git a/subiquity/models/filesystem.py b/subiquity/models/filesystem.py
index 0d9220dc..71cc5ee6 100644
--- a/subiquity/models/filesystem.py
+++ b/subiquity/models/filesystem.py
@@ -32,6 +32,7 @@ import more_itertools
 
 from curtin import storage_config
 from curtin.block import partition_kname
+from curtin.swap import can_use_swapfile
 from curtin.util import human2bytes
 
 from probert.storage import StorageInfo
@@ -1814,8 +1815,9 @@ class FilesystemModel(object):
 
     def should_add_swapfile(self):
         mount = self._mount_for_path('/')
-        if mount is not None and mount.device.fstype == 'btrfs':
-            return False
+        if mount is not None:
+            if not can_use_swapfile('/', mount.device.fstype):
+                return False
         for swap in self._all(type='format', fstype='swap'):
             if swap.mount():
                 return False
diff --git a/subiquity/models/tests/test_filesystem.py b/subiquity/models/tests/test_filesystem.py
index 3a990a05..7c563d55 100644
--- a/subiquity/models/tests/test_filesystem.py
+++ b/subiquity/models/tests/test_filesystem.py
@@ -1237,14 +1237,18 @@ class TestSwap(unittest.TestCase):
         self.assertTrue(m.should_add_swapfile())
 
     @parameterized.expand([
-        ['ext4', True],
-        ['btrfs', False],
+        ['ext4', None, True],
+        ['btrfs', 5, True],
+        ['btrfs', 4, False],
+        ['zfs', None, False],
     ])
-    def test_should_add_swapfile(self, fs, expected):
+    def test_should_add_swapfile(self, fs, kern_maj_ver, expected):
         m, d1 = make_model_and_disk(Bootloader.BIOS)
         d1p1 = make_partition(m, d1)
         m.add_mount(m.add_filesystem(d1p1, fs), '/')
-        self.assertEqual(expected, m.should_add_swapfile())
+        with mock.patch('curtin.swap.get_target_kernel_version',
+                        return_value={'major': kern_maj_ver}):
+            self.assertEqual(expected, m.should_add_swapfile())
 
     def test_should_add_swapfile_has_swappart(self):
         m, d1 = make_model_and_disk(Bootloader.BIOS)