We characterize optimal unconventional monetary and fiscal-financial policies against supply- and demand-driven liquidity traps within a tractable New Keynesian model featuring a cash-in-advance constraint and a monetary policy cost channel. Deposit subsidies circumvent the inflation-output trade-off arising from stagflationary shocks and supply-driven liquidity traps by enabling negative nominal interest rates. Additionally, deposit taxes facilitate modest interest rate hikes to escape demand-driven deflationary traps. Notably, discretionary and commitment policies with deposit taxes / subsidies deliver virtually equivalent welfare gains, rendering time-inconsistent forward guidance schedules unnecessary. We also derive robust and implementable optimal policy rules when the sources of shocks are unknown.