You will need to be a little more choosy as to what you put out for the birds, if you put out fat balls and smaller seeds rather than bread and scraps etc, you will encourage the smaller birds, specific seeds will attract specific birds, ask at you pet shop.
RATTERs given you a good answer, especially about the fat balls, about the biggest you'll get on those is Starlings, but regarding seeds, the larger birds are mainly groundfeeders, and you can't really stop them.
Alternatively ... find something the bigger birds really like and feed them elsewhere (other end of the garden).
I don't do this, just read it somewhere.
Personally I don't mind the big birds vising the garden ... Jackdaws can be very entertaining when there's 30 of them trying to get on the table at 5 a.m. ... (and noisy too, dammit)
I agree with Naz's point. I have the fat balls and 'nut bags' etc, but put bread, bacon fat and the like on one specific shed roof for the magpies, crows and jacks etc.... We have all sorts of birds in our garden and all are a joy to watch... the best one being a wood pecker, not sure what to put out for him, he just enjoys destroying my apple tree!!!!!
I find that crows can and do eat anything. They love fat balls and have learned how to eat from nut feeders and from seed feeders. Don't put saucers under your feeders as they find this arrangement most helpful!
They are, however, scaredycats so if you clap your hands they fly off and the little ones just stay where they are and get tucked into the food.
Try a niger (pronounced nyjar) seed feeder. Niger seed is thistle seed, small black seeds. This attracts goldfinches and other small finchs (mainly because it only has small holes which the goldfinches can get their beaks into, and the bigger birds can't). They have a little hooky type beak which picks up the small seed, and the other birds drop it if they try to pick it up. They will soon learn where to come, although it may take a few weeks for the word to get round that you have got it in your garden. Then they will tell all their friends, and you will be able to watch them squabbling over it and bringing their babies.