Recent research finds that deposit market competition influences the transmission of monetary policy to deposits and the real economy. We present two circumstances under which this relationship does not hold (i) low interest rate environments and (ii) low reliance on deposit financing. We document how in such circumstances deposit competition does not differentially affect the transmission of monetary policy to deposits. Interestingly, we document how aggregate economic activity is still differentially affected depending on bank competition. This suggests an alternative mechanism linking bank competition and aggregate effects. Overall, our findings suggest that low interest rates and low reliance on deposit funding dampen the influence of deposit market competition for the transmission of monetary policy.