Accurate assessments of bank deposit market power are essential for antitrust and monetary policy. Regulators and researchers currently assess market power under the assumption that all consumers consider every bank operating in a given geographic region. However, in practice, consumers only consider a small fraction of the available banks. I propose a new model of bank deposit competition that specifically accounts for this limited consideration. I estimate the model for the twenty largest US Metropolitan Statistical Areas over 2004 to 2018 using rich data on bank deposit interest rates, bank advertising, and the distance between consumers and bank branch locations. I find that accounting for consumers' limited consideration of banks shows that current assessments underestimate the market power of online direct banks, poorly capture how market power contributes to heterogeneous bank pass through of federal funds rate changes, and support an inefficient proposal for strengthening bank deposit competition. Whereas current assessments recommend further bank deregulation, I demonstrate that a better plan for strengthening competition is to facilitate the launch of an online direct bank by a major technology company.