Are you familiar with Moka Pots? According to Wikipedia, they are sold in 1,3,6,9,12 shot sizes -- but I think the 3 is the most common. I rarely see large Mokas. You're not really throwing much out.
FWIW the aeropress is a very good alternative to french presses, significantly simpler cleaning (just pop the coffee plug in the compost/trash and rinse the components), almost no fines (if you use paper filters). Though the rest of the operations (grinding coffee, pouring boiling water in the press and pressing down) are the same.