diff --git a/mount/mount.go b/mount/mount.go
index 883f8df3..4a7bb27b 100644
--- a/mount/mount.go
+++ b/mount/mount.go
@@ -17,15 +17,26 @@ func Mount(device, target, mType, options string) error {
 	return mount(device, target, mType, uintptr(flag), data)
 }
 
-// Unmount lazily unmounts a filesystem on supported platforms, otherwise
-// does a normal unmount.
+// Unmount lazily unmounts a filesystem on supported platforms, otherwise does
+// a normal unmount.  If target is not a mount point, no error is returned.
 func Unmount(target string) error {
 	return unmount(target, mntDetach)
 }
 
-// RecursiveUnmount unmounts the target and all mounts underneath, starting with
-// the deepsest mount first.
+// RecursiveUnmount unmounts the target and all mounts underneath, starting
+// with the deepest mount first. The argument does not have to be a mount
+// point itself.
 func RecursiveUnmount(target string) error {
+	// Fast path, works if target is a mount point that can be unmounted.
+	// On Linux, mntDetach flag ensures a recursive unmount.  For other
+	// platforms, if there are submounts, we'll get EBUSY (and fall back
+	// to the slow path). NOTE we do not ignore EINVAL here as target might
+	// not be a mount point itself (but there can be mounts underneath).
+	if err := unmountBare(target, mntDetach); err == nil {
+		return nil
+	}
+
+	// Slow path: get all submounts, sort, unmount one by one.
 	mounts, err := mountinfo.GetMounts(mountinfo.PrefixFilter(target))
 	if err != nil {
 		return err
diff --git a/mount/unmount_unix.go b/mount/unmount_unix.go
index 1d1afeee..924d059a 100644
--- a/mount/unmount_unix.go
+++ b/mount/unmount_unix.go
@@ -4,8 +4,12 @@ package mount
 
 import "golang.org/x/sys/unix"
 
+func unmountBare(target string, flags int) error {
+	return unix.Unmount(target, flags)
+}
+
 func unmount(target string, flags int) error {
-	err := unix.Unmount(target, flags)
+	err := unmountBare(target, flags)
 	if err == nil || err == unix.EINVAL {
 		// Ignore "not mounted" error here. Note the same error
 		// can be returned if flags are invalid, so this code
diff --git a/mount/unmount_unsupported.go b/mount/unmount_unsupported.go
index eebc4ab8..4d6073ec 100644
--- a/mount/unmount_unsupported.go
+++ b/mount/unmount_unsupported.go
@@ -2,6 +2,10 @@
 
 package mount
 
-func unmount(target string, flag int) error {
+func unmountBare(_ string, _ int) error {
+	panic("Not implemented")
+}
+
+func unmount(_ string, _ int) error {
 	panic("Not implemented")
 }