Shadows in OpenGL 2D game

Hi,
it's me again with my never-ending questions... :)
Now that I have come rather far with my game engine, I thought that the objects (just textured GL_QUADS) on the screen look a bit dull, so I wanted to make some dropdown shadows. What I did to make it look rather realistic was to take objects texture, flip it, rotate it and apply to a quad which is changing position and scaling while the sun moves. That looks rather good with trees and other objects where the shadow is mostly covered with the object itself. (look at this picture :http://www.home.no/mathfan/tree.png) But when it comes to small objects which are not able to cover the artifacts which this shadow calculation causes, the shadows look awful...(look at this one:http://www.home.no/mathfan/gravestone.png)
You can of course turn off the shadowing of this objects, but then they look quite out of place in a scene full of shadowed objects.

So my question is: am I able to calculate a shadow an object drops only by looking at the textured quad which represents the object or its texture data(remember, this is a 2D game which uses glOrtho)? This shadow calculation doesn't have to be very accurate, I'm just wondering if anyone has an idea of how to do it better then the my original calculation.

thanx