When my program uses directx7, rendering artifacts are produced on models which
closely overlap each other. Close together meaning, for example, two planes
with different shaders stacked closely on top of each other, but not touching
(close, but different, z-values). I can describe the artifacts as jagged
horizontal lines, somewhat like interlaced video. Lines appear to be the lower
model "showing through" the upper model.

The further away from the camera the overlapped models are, the greater the
problem. Though at close distances and very far distances, the problem is less
or gone. OpenGL does not show this problem at all. Problem shows on different
systems, not just mine. Is this just the way it is? Or can I remedy it somehow?