Ok I know this seems pretty obvious but it never really hit home until recently.
First you are going to fill from the edges in right. Often you will be left with a 2 piece hole that requires 2 SPECIFIC pieces.
Lets just say this hole can be filled with a common piece and a rare piece. Just say you already have the common piece in your box. DO NOT use it yet! Leave it in your box until the puzzle is about to fall apart. That delay will increase your chance of getting that rare piece.
I find this helps as well. Focus on 2 puzzles at once. Do not try and fill all 4 at the same time. If you do you will find you need specific pieces in all 4 puzzles and no where to put them. This is really just an opinion but worth a try.
My leg carp would be higher if my lame track point didn't like to move my mouse all over the screen. T_T