We show that makeup strategies, such as average inflation targeting and price-level targeting, can be more effective than a flexible inflation targeting strategy in overcoming the obstacles created by the effective lower bound in a heterogeneous agent New Keynesian (HANK) model. We also show that the macroeconomic stabilization benefits from such alternative strategies can be substantially larger in a HANK environment than in a representative agent New Keynesian model. We argue that gains in employment outcomes from switching to an alternative strategy would generate disproportionate improvements for historically disadvantaged households and thus have potentially long-lasting effects on the economic well-being of these groups.