heres an idea
That is the problem with compartment fly boxes. Your flies get stuck together, and you are likely to drop flies in the river trying to get one apart. In my opinion, the compartment flyboxes serve best for strike indicators, hooks, splitshot, or beads.
I am a fan of C&F flyboxes:
You can fit a ton of flies in them, and they keep your flies organized and neat. The slits are very snug too, more so than regular foam.