The floss boxes I use are similar to what Dean suggests above, see:
http://ep.yimg.com/ay/craftersmarket/flo...izer-6.gif .
As for Zaarin's question, generally speaking I can dig or stir around if I'm looking for a common counter (e.g. 8xGREN in a compartment containing Heer foot units): at worst (or for leader draws), one simply pulls out the bunch, searches through, then replaces the unused ones.
For me, the convenience is in: security of storage in the box (the box and counters can't easily be "crushed" and the lid is secure); easy stacking of the boxes; and easy ID of the box contents via permanent marking. So, for example, to play an
Fronte Russo scenario, I simply pull the: (i) AFD+FR+SF; (ii) EFD; and (iii)markers boxes.