For example, let's say I am designing a car and I need it to be as light as possible for increased fuel economy but as strong as possible for passenger safety. By making it stronger I make it heavier - by making it lighter I make it weaker. One precludes the other.
So how do I describe this dilemma? Stronger is xxxxx with lighter.
Incompatible, divergent, 'at odds', 'diametrically opposed' all come to mind but none of those are the one I just can't get off the tip of my tongue.