This paper proposes two approaches for utilizing the information in multiple entity groups and multiple views to reduce the number of hypotheses passed to the verification stage in a model-based object recognition system employing invariant feature indexing (P. J. Flynn and A. K. Jain, CVGIP: Image Understand. 55(2), 1992, 119-129). The first approach is based on a majority voting scheme that keeps track of the number of consistent votes cast by prototype hypotheses for particular object models. The second approach examines the consistency of estimated object pose from multiple groups of entities (surfaces) in one or more views. A salient feature of our system and experiment design compared to most existing 3D object recognition systems is our use of a large object database and a large number of test images. Monte Carlo experiments employing 585 single-view synthetic range images and 117 pairs of synthetic range images with a large CAD-based 3D object database (P. J. Flynn and A. K. Jain, IEEE Trans. Pattern Anal. Mach. Intell. 13(2), 1991, 114-132) show that a large number of hypotheses (about 60% for single views and 90% for multiple views on average) can be eliminated through use of these approaches. The techniques have also been tested on several real 3D objects sensed by a Technical Arts 100X range scanner to demonstrate a substantial improvement in recognition time.