This paper treats the problem of describing the behavior of a function u bounded and harmonic in a disk, when its behavior is known on a portion B of the disk that contains an open set. If /u/ is bounded by one on the disk and bounded by E on B, then /u/ is bounded at the origin by Kie ,K2>0. The method is to complexify u, use a lemma of Carleman to bound /u/ in a neighborhood of the origin, and use a three-circle theorem of Miller to bound /u/ in the rest of the disk.