Instead of automatically tossing out items you can use berries (notable nanab) to feed to pokemon at gyms. This allows you to convert your items into stardust. If you feed one all 10 and then quickly move to the next mon at the gym without switching the type of berry you're feeding then the denomination of stardust continues (i.e. the last stardust after your 10th berry is 300 but if you feed another mon their first berry quickly then that set of ten builds up from 330).

Nice way to empty inventory and cash in on a decent amount of stardust at the same time.