I believe you will have to squeeze more than a few times. I find that the first few squeezes do little but break up the mass in the sponge. Subsequent squeezes will remove far more crud than the first few. I clean them quite vigorously until nothing more comes out of them. The nitrifying bacteria are basically glued to the sponge and don't come off that easily.
Join a fish club. Don't have one in your area? Start one.