Recognition via alignment is a method for recognizing the general class of rigid objects, which includes vehicles, known terrain, and buildings. A candidate alignment transformation is computed from a minimal set of three corresponding points from model to image, and the transformation and model are accepted only after an expensive verification step. Methods are given here which can dramatically reduce the amount of computation required for recognition by alignment. First, the use of aspects is proposed to cut down on the combinatorics of point correspondence. Secondly, two practical constraints on orientation and size are shown to eliminate many alignment candidates before the expensive verification step. Simulations are reported which show the usefulness of the proposed methods in the context of automatic target recognition.