I am creating an app icon that has a drop shadow.

When I resize the icon to some smaller pixel sizes to use in an app (around 20 x 20 pixels) the object transforms fine except for the shadow.  I have checked the 'Scale Strokes & Effects' box in the transform window. 

It seems the minimum size for the offsets of the drop shadow is one pixel regardless of what I type in the drop shadow box for yoffset and xoffset.

Is there anyway to get the shadow effect on a very small object?  I know it will hardly be noticeable for such a small object but I prefer not to delete the shadow every time I resize the object.