Stop starlings but encourage nuthatches?

We are inundated by starlings who aggressively hog the feeders. They have destroyed all the uncaged gravity/hopper seed feeders but luckily the metal cages protect the nut feeders. Does anyone have knowledge of which gravity/hopper seed feeders will prevent the starlings feeding but still allow the nuthatches to feed? The starlings ignore the bog standard peanut feeders, thankfully, as the tits and woodpeckers use them.