unsupported glPolyonOffset

I’ve got a piece of code, where I have
successfully used glPolygonOffset. On an
“improved” graphics card, this function is
not enabled.

I used it to begin with because of zbuffer precision. There could potentially be (in reality) two objects exactly in the same space. The offset was used to help the z, so they wouldn’t flicker.

I have heard of people clearing the zbuffer,
and rescaling it. Is there a better way to do this??