Should asset testing be used in means-tested programs? These programs target low-income people, but low income can result not only from low productivity but also from low labor supply. We aim to show that in the asymmetric information environment, there is a positive role for asset testing. We focus on Medicaid, one of the largest means-tested programs in the US, and we ask two questions: 1) Does Medicaid distort work incentives? 2) Can asset testing improve the insurance-incentives trade-off of Medicaid? Our tool is a general equilibrium model with heterogeneous agents that matches many important features of the data. We find that 23% of Medicaid enrollees do not work in order to be eligible. These distortions are costly: if individuals' productivity was observable and could be used to determine Medicaid eligibility, this results in substantial ex-ante welfare gains. When productivity is unobservable, asset testing is effective in eliminating labor supply distortions, but to minimize saving distortions, asset limits should be different for workers and non-workers. This work-dependent asset testing can produce welfare gains close to the case of observable productivity.