This paper presents an inventory-control model which includes a Markovian model of the supply system. As that system evolves over time, so do the replenishment leadtimes. The optimal policy has the same structure as in standard models, but its parameters change dynamically to reflect current supply conditions. In this setting, contrary to conventional wisdom, a longer leadtime does not necessarily imply more inventory. The leadtime is important, but so is a concept we call order coverage.