MadMonkey: Good suggestion. It has been proposed before, and I still like it. But instead of giving byes random, I suggest doing the byes randomly only if the tournament is selected to not sort by rating. For tournaments which sort by rating, byes should go to the highest ranked players (just like it would happen in tennis or chess). So, if you have 13 players in a 16 game elimination tournament, the top 3 rated players would get byes.

And, once you have a system of byes, it should be easy to make setting the number of players for elimination tournaments optional (just as regular tournaments have optional lower and upper limits). You could make an elimination tournament with no set number of players. If at the deadline, there are 27 players signed up, you'll have a 5 round tournament, with 5 byes in the first round. If only 12 people signed up, you'll have a 4 round tournament, with 4 byes in the first round.