There is a growing body of evidence that interest rate spreads in Africa are higher for big banks compared to small banks. One concern is that big banks might be using their market power to charge higher lending rates as they become larger, more efficient, and unchallenged. In contrast, several studies found that when bank size increases beyond certain thresholds, diseconomies of scale are introduced that lead to inefficiency. In that case, we also would expect to see widened interest margins. This study examines the connection between bank size and efficiency to understand whether that relationship is influenced by exploitation of market power or economies of scale. Using a panel of 162 African banks for 2001-2011, we analyzed the empirical data using instrumental variables and fixed effects regressions, with overlapping and non-overlapping thresholds for bank size. We found two key results. First, bank size increases bank interest rate margins with an inverted U-shaped nexus. Second, market power and economies of scale do not increase or decrease the interest rate margins significantly. The main policy implication is that interest rate margins cannot be elucidated by either market power or economies of scale. Other implications are discussed.