Transparent objects and shadow intensity

Hi everyone,
I am having a bit of a problem with shadows cast by transparent objects. The simplest working example I can think of is a wedge shape with light coming from above, casting a shadow on a plane below. The wedge is partially transparent, and theoretically it should cast a light shadow where it is thinnest and a gradually darker shadow as it gets thicker.
What I have tried:
Blender render using Transparency and playing around with the values of both Z-transparency and Raytrace transparency.
Cycles render trying both the Light path is shadow Ray as well as Volume absorption.
I can never seem to get a transparency which depends on the thickness. I also tried to make a simpler (maybe) solution with two cubes of different thickness but of the same material, and they too cast the same shadow.
I guess maybe I should be playing with the material of the receiving object as well, but I have no clue of how to make that work.
Does anyone have any idea, or a simple solution I just missed.