Line drawing order

Im using GL lines to darw the lines in a modeller im making. I want the currently selected face to be a different colour, but other faces share some of the same lines.

Is there a way of deciding the order to draw to the screen so that the currently selected face is always drawn over the others? ive tried drawing in different orders, but it doesnt seem to make a difference

Depends on the way you store and draw the faces of the model.
How about first drawing all of them in the regular color and then redrawing just the selected face in the ‘selected’ color.
You will have to do someting to either the depth test or the polygon offset to ensure the selected face is actually drawn.