The alignment method  is a model-based object recognition technique that determines possible object transformations from three hypothesized matches of model and image points. For images and/or models with many features, the running time of the alignment method can be large. This paper presents methods of reducing the number of matches that must be examined. The techniques we describe are: Using the probabilistic peaking e ect  to eliminate unlikely matches (implemented in a probabilistic indexing system ) and eliminating groups of model points that produce large errors in the transformation determined by the alignment method. Results are presented that show we can achieve a speedup of over two orders of magnitude while still nding a correct alignment.