The nestbox hole size for an Eastern Bluebird is 1 1/2 inches. Chickadees and Titmouse both like the size although they are smaller. After a nest is built however a guard can be added without a problem. Reducing the size by 1/4 inch will keep larger birds out.
You can buy these guards but it is easy to make them. If you have the tools you can make them from wood. Sand the inside until it is smooth. This will keep the feathers from being damaged. If you lack the tools or time then cardboard and a box knife will work as a quick fix. Just attach them with tacks or even duct tape.
I owe my Bluebird Mentor, Evelyn, for teaching me how to handle this problem. To learn more about the uses of Hole Guards. Check out this link. Sialis is a great site to learn about Bluebirds and the problems with trying to help them to thrive.
I took this picture from my window last fall of this beautiful male. He posed for me!