A Health Savings Account (HSA) is a tax-advantaged savings account available only to households with high-deductible health insurance. This paper provides initial answers to two questions related to HSAs: 1) How should a household determine its annual contributions as the health status of its members evolve, and 2) do current contribution limits provide households with the flexibility to use HSAs efficiently? To answer these questions, we formulate the household’s problem as one of determining a contribution strategy for minimizing total expected discounted medical costs. Costs are modeled as varying from year to year according to a Markov process where the state reflects the household’s health status. A dynamic threshold policy, in which the contribution each year brings the HSA balance to a health state-dependent threshold, is derived. This is compared to a simpler static threshold policy in which the annual save-up-to level is state-independent (equal to the plan’s out-of-pocket maximum) with contributions further capped by an annual limit. The cost model is calibrated to data from the 2002-2014 Medical Expenditure Panel Survey (MEPS). Policies are then derived and tested for a typical HSA-eligible plan. The results show that: a) The dynamic policy has 1%-27% lower total costs than the static one, though the static policy with a sufficiently high annual limit is a worthy alternative in the absence of personalized analytical guidance; b) a two-tiered tax-free contribution limit, in which the contribution size is unrestricted up to a certain HSA balance (tied to the plan’s out-of-pocket maximum) and restricted beyond it, is necessary for households to make efficient use of HSAs.