This paper utilizes a new flow measure of the true output of bank services to analyze the impact of mergers on the cost and productivity of Bank Holding Companies (BHCs) over the period 1987-1999. It shows that there are conceptual problems in the output measures used in previous studies, which may be the reason for their paradoxical findings: Bank mergers are estimated to lead to significant increases in profit, without cost savings or increases in market power. This paper also points out the problematic understanding of diversification in previous studies. To remedy these problems, this paper uses a new measure that accounts coherently for risk in measuring bank service output and recognizes that the funds banks borrow and lend are a special intermediate input. Once one accounts for the better diversification resulting naturally from mergers, the commonly used, book-value-based output measure shows little improvement in cost productivity. In contrast, the new flow measure of bank output shows more improvement, although it is still insignificant-partly because the sample size is relatively small. The gap widens further when one corrects for possible bias in the new output estimate. Thus, the new measure of bank output has the potential to resolve the paradox found in the existing literature, by showing that mergers do lead to cost savings.