  A method is presented for estimating the background at a given location on a
sky map by interpolating the estimated background from a set of concentric
annuli which surround this location. If the background is nonuniform but
smoothly varying, this method provides a more accurate (though less precise)
estimate than can be obtained with a single annulus. Several applications of
multi-annulus background estimation are discussed, including direct testing for
point sources in the presence of a nonuniform background, the generation of
"surrogate maps" for characterizing false alarm rates, and precise testing of
the null hypothesis that the background is uniform.
