Most birds like about 1 inch of water. I would try not filling it full and see what happens.

We put a brick in the middle of ours. They can stand on it and test the depth of the water or stand there and get a drink.

Hummingbirds like very shallow water. They also like splashing water.

http://www.homestoriesatoz.com/outdoor/diy-bird-bath.html

I am going to make one with a solar pump, not quite like the above, but more natural-looking cascading bubbling fountain.

I wondered why the birds drank out of the humdinger ant cups instead of the birdbath. Will try the brick and not filling as full. Thanks for the suggestions.

A standing birdbath on the patio has gotten only limited use for several years. Also far from the house and a pain to keep clean. This year I bought one of those deck-railing birdbaths. It's only steps from the kitchen so easy to keep clean in hot weather, and it's being used for both drinking and baths. The red-headed sparrows that drink from the ant cups unfortunately still use the ant cups as well as the birdbath. Well who wouldn't like to have two sources of water? :)

I thought a brick too high so used a small flagstone type stone and a couple of 3-4 inch river rocks in the middle. However, they drink from the edge.