jit.lcd flickering

Hello everybody, I have a very simple question but I don't really know what the simplest solution could be.

While drawing to a jit.lcd with paintpoly objects, the area where two paintpoly objects overlap begins to flicker back and forth between the two colors because the information is being sent simultaneously. Ideally, I would like the objects to 'layer' over each other, similar to a layer in Photoshop.
Before I spend a large amount of time doing the wrong thing, I thought I might ask here. While browsing the forums, I've heard solutions to somewhat similar problems such as using OpenGL, 3-dimensional matrices or alphablend. Can someone offer me some advice? I've attached an example patch to exemplify my problem.