[Gimp-user] How to make transparency gradiate?

[Keith Purtell <kpurtell imirus com>]

A client has supplied a logo for Web display (PNG). The logo background is white and needs to become transparent. I've done this in GIMP no problem with simple graphics. However this one features design elements that cast a pale gray shadow onto the white background. Not sure how to make the transparent background play nice with the shadow area?  

If it helps, the background color where this logo will be displayed is pale gray with a bit of blue tint.