MINPRAN accurately reconstructs range data taken from scenes that produce: (1) large numbers of outliers, (2) points from multiple surfaces interspersed over large image regions, and (3) extended regions containing only bad data. MINPRAN uses random sampling to search for fits that minimize a criterion function which models the probability that a fit could be due to random bad points. In a previous paper [TR93-21] , we showed that MINPRAN finds accurate fits, even when more than half of the data are bad; and it avoids hallucinating fits when all of the data are bad. However, we also showed that MINPRAN often favors a single fit bridging multiple surfaces when the data in an image region arise from one or more surfaces. In this paper, we extend MINPRAN in two ways to handle the problem of multiple fits in a region: (1) it now searches for and compares two disjoint fits to the single best fit in a region, and (2) it reconstructs the best values of each data point, re-applies the criterion function to each fit using only the inliers that remain consistent with that fit, and eliminates fits that appear random. The new version of the algorithm, called MINPRAN2, produces extremely good results on difficult range images and intensity images that have been corrupted with a large number of random bad values.