Multi-output measures of market power have become increasingly important in banking, since banks have been broadening their business from interest-bearing activities to fee-based activities. For the analysis of a multi-output bank's market power, it is often attractive to calculate an average measure of market power over the various outputs. The contribution of this study's theoretical part is twofold. First, we propose a weighted-average Lerner index that has relatively mild data requirements. Second, we compare our weighted-average Lerner index to an alternative Lerner index that has recently gained popularity as a multi-output measure of market power in the banking literature. We show that this alternative Lerner index has no sensible economic interpretation in a multi-output setting and underestimates a multi-output firm's average degree of market power. The empirical part of this study illustrates the two Lerner indices using U.S. banking data covering the period 2000 - 2016.