A seller wishes to sell multiple goods by a deadline, for example, the end of a season. Potential buyers enter over time and can strategically time their purchases. Each period, the profit-maximizing mechanism awards units to the buyers with the highest valuations exceeding a sequence of cutoffs. We show that these cutoffs are deterministic, depending only on the inventory and time remaining; in the continuous-time limit, the optimal mechanism can be implemented by posting anonymous prices. When incoming demand decreases over time, the optimal cutoffs satisfy a one-period-look-ahead property and prices are defined by an intuitive differential equation.