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Prior research under a variety of conditions has shown the CORI algorithm to be one of the most effective resource selection algorithms, but the range of database sizes studied was not large. This paper shows that the CORI algorithm does not do well in environments with a mix of "small" and "very large" databases. A new resource selection algorithm is proposed that uses information about database sizes as well as database contents. We also show how to acquire database size estimates in uncooperative environments as an extension of the query-based sampling used to acquire resource descriptions. Experiments demonstrate that the database size estimates are more accurate for large databases than estimates produced by a competing method; the new resource ranking algorithm is always at least as effective as the CORI algorithm; and the new algorithm results in better document rankings than the CORI algorithm.