I read something in Birds and Blooms about this issue. The article dealt with sparrows specifically, but maybe it would work for wrens as well. It recommends drilling a 2" hole in the top of the birdhouse. Sparrows don't like the light, but bluebirds don't mind. I hope this helps. Oh, and to deter wasps from moving in, I've heard you can line the top inside with aluminum foil. Good luck~