The quantitative easing (QE) policies implemented in recent years by central banks have had a profound impact on the working of money markets, giving rise to large excess reserves and pushing down key interbank rates against their floor – the interest rate on reserves. With macroeconomic fundamentals improving, central banks now face the dilemma as to whether to maintain this large balance sheet/floor system, or else to reduce their balance sheet size towards pre-crisis trends and operate traditional corridor systems. We address this issue using a New Keynesian model featuring heterogeneous banks that trade funds in an interbank market characterized by matching frictions. In this environment, balance sheet expansions push market rates towards their floor by slackening the interbank market. A large balance sheet regime is found to deliver ampler ‘policy space’ by widening the steady-state distance between the interest on reserves and its effective lower bound (ELB). Nonetheless, a lean-balance-sheet regime that resorts to temporary but prompt QE in response to recessions severe enough for the ELB to bind achieves similar stabilization and welfare outcomes as a large-balance-sheet regime in which interest-rate policy is the primary adjustment margin thanks to the larger policy space.