Transparent top-level windows

I would like to create a top-level (i.e., not WS_CHILD) window with transparency. However, I don't want it to be a simple mask, where a given pixel is either fully transparent or fully opaque. And I don't want it to be such that the entire window has some alpha level to it. Rather, I'd want the window to essentially be entirely transparent, with a bitmap drawn to it with an alpha channel, such that the bitmap blends with whatever windows may be behind it. Picture, say, a sunburst, where an image's own alpha blends from opaque to fully transparent outward from the center.

I have found two methods that both get close to what I want to do, but not quite. Using regions, I can cut out a section that is drawn completely transparent. Using layered windows, I can also do something similar (or can even make the entire window slightly transparent, but that is not what I want at all). I have looked into other styles, such as WS_EX_TRANSPARENT and WS_EX_COMPOSITE, but to no avail.

I can get this kind of effect to work just fine on child windows, since they are blending with their parent windows within their parent's region. Getting it to work similarly for top-level windows continues to elude me.

I know this can be done, as people have assured me they've seen it in other programs. I feel like I'm just not fully understanding something simple here about painting windows.