diff --git a/module/zfs/zvol.c b/module/zfs/zvol.c
index 623fb9b221..2547602204 100644
--- a/module/zfs/zvol.c
+++ b/module/zfs/zvol.c
@@ -1603,6 +1603,9 @@ zvol_alloc(dev_t dev, const char *name)
 	if (volmode == ZFS_VOLMODE_DEFAULT)
 		volmode = zvol_volmode;
 
+	if (volmode == ZFS_VOLMODE_NONE)
+		return (NULL);
+
 	zv = kmem_zalloc(sizeof (zvol_state_t), KM_SLEEP);
 
 	list_link_init(&zv->zv_next);
diff --git a/tests/zfs-tests/include/libtest.shlib b/tests/zfs-tests/include/libtest.shlib
index 88594c2010..be71c0d75d 100644
--- a/tests/zfs-tests/include/libtest.shlib
+++ b/tests/zfs-tests/include/libtest.shlib
@@ -3425,7 +3425,7 @@ function swap_setup
 	typeset swapdev=$1
 
 	if is_linux; then
-		log_must mkswap $swapdev > /dev/null 2>&1
+		log_must eval "mkswap $swapdev > /dev/null 2>&1"
 		log_must swapon $swapdev
 	else
 	        log_must swap -a $swapdev
diff --git a/tests/zfs-tests/tests/functional/zvol/zvol_misc/zvol_misc_volmode.ksh b/tests/zfs-tests/tests/functional/zvol/zvol_misc/zvol_misc_volmode.ksh
index 5cf6a60b3b..934d8942f0 100755
--- a/tests/zfs-tests/tests/functional/zvol/zvol_misc/zvol_misc_volmode.ksh
+++ b/tests/zfs-tests/tests/functional/zvol/zvol_misc/zvol_misc_volmode.ksh
@@ -40,7 +40,8 @@
 # 4. Verify "volmode=dev" hides partition info on the device
 # 5. Verify "volmode=default" behaves accordingly to "volmode" module parameter
 # 6. Verify "volmode" property is inherited correctly
-# 7. Verify "volmode" behaves accordingly to zvol_inhibit_dev (Linux only)
+# 7. Verify "volmode" behaves correctly at import time
+# 8. Verify "volmode" behaves accordingly to zvol_inhibit_dev (Linux only)
 #
 # NOTE: changing volmode may need to remove minors, which could be open, so call
 #       udev_wait() before we "zfs set volmode=<value>".
@@ -54,6 +55,7 @@ function cleanup
 	log_must zfs inherit volmode $TESTPOOL
 	udev_wait
 	sysctl_inhibit_dev 0
+	sysctl_volmode 1
 	udev_cleanup
 }
 
@@ -194,10 +196,18 @@ log_must zfs set volmode=full $TESTPOOL
 verify_inherited 'volmode' 'none' $SUBZVOL $VOLFS
 blockdev_missing $SUBZDEV
 blockdev_exists $ZDEV
+
+# 7. Verify "volmode" behaves correctly at import time
+log_must zpool export $TESTPOOL
+blockdev_missing $ZDEV
+blockdev_missing $SUBZDEV
+log_must zpool import $TESTPOOL
+blockdev_exists $ZDEV
+blockdev_missing $SUBZDEV
 log_must_busy zfs destroy $ZVOL
 log_must_busy zfs destroy $SUBZVOL
 
-# 7. Verify "volmode" behaves accordingly to zvol_inhibit_dev (Linux only)
+# 8. Verify "volmode" behaves accordingly to zvol_inhibit_dev (Linux only)
 if is_linux; then
 	sysctl_inhibit_dev 1
 	# 7.1 Verify device nodes not are not created with "volmode=full"