Abstract: A bracket for supporting a fence rail includes a hollow body having an open-topped cavity and an end wall with a cross-shaped aperture through which a bolt is passed into a fence post. The angularity of the body with respect to the post surface is adjusted by installing one or more tapered spacers between the body and the post. The spacers have nesting bosses and recesses, and offset slots through which the bolt passes. One surface of the end wall has a spherical shape so that the head of the bolt seats flat, regardless of the angularity which has been established.