Armature problem

I’m making my own game character and i’m having some trouble with the armatures. Because of the way it exports, my game character is limited to the “old” way of rigging, I.e, parenting the mesh to the armature and playing around with the vertices. The problem i’m having is the distortion of joints like the elbow joint when I rotate the bones of my mesh to large angles (above 90 degrees). They look squashed and disgusting.

Unfortunately I’m not “allowed” to use modifiers to solve this problem, or anything fancy for that matter. All i’m allowed to do is use “normal bones” and the vertices of the mesh.

Oh and by the way, I tried two different methods to solve this problem. The first was to loop cut the vertices around the joint, which only helped marginally. The second was to add a very small bone right at the joint, which just made the problem worse.

So this is my plight, can anyone help? (sorry if the question seems juvenile).

Edit: Anyone? Anyone at all??? Surely someone must know how to rig a mesh so that when you rotate the bones they don’t get deformed?