We no longer feed the birds with seed. We stopped this practice over a year ago because of the rodent problem. Squirrels are bad enough, but the other ones which come at night are even worse. We were making it too easy for them.
Now we feed the birds by smearing peanut butter on the deck railing. This has the advantage of making it harder for the squirrels to dominate the feeding stations, and there is nothing to fall to the ground for the mice and rats to eat. So far, the peanut butter seems to appeal to a limited variety of local birds: cardinals in particular seem to appreciate it.
In the image above you can see Mema putting out the peanut butter. About six feet to her right you can see an impatient male cardinal waiting for her to leave. The cardinals seem to recognize her: as soon as she comes into the kitchen in the morning, they fly up to the big glass doors and call to get her attention. When she goes out with the peanut butter, they sit nearby and seem relatively fearless.