How to make a little wiggle room for the collision?

In my game, I have two objects: one that is just a cube, and one that is shaped so that the cube will fit into it. The problem is that when they collide, I want them to stick to each other but I want to make it so that if they were close to going together, they will go ahead and fit together instead of stopping about halfway through. Any suggestions? Sorry if this was hard to understand, I don't really know how to word it.