RegisterCompleteObjectUndo with mesh.vertices

If you want to undo changes made to a mesh's vertices using the built-in Undo class, how do you go about it?

I tried:

Code (CSharp):

1. Mesh m = target.GetComponent<MeshFilter>().sharedMesh;
2. Undo.RegisterCompleteObjectUndo( m, "Changed mesh" );
3. m.vertices = someNewVerts;

and although "Changed mesh" does appear next to Undo in the Edit menu, it doesn't seem to work. I also tried registering the parent GameObject, which also didn't work.

I did do one test of modifying the GameObject's name, and that was undoable. But changes to mesh properties haven't been. I know they're all getters/setters and maybe that's why? In that case, is there a recommended way to do this, or should the wizard making these changes just offer its own history and restore functionality?

(applies to 2017.2.0p4)