As the time between the decision about what to produce and the moment when demand is observed (the decision lead time) increases, the demand forecast becomes more uncertain. Uncertainty can increase gradually in decision lead time, or can increase as a dramatic change in median demand. Whether the forecast evolves gradually or in jumps has important implications for the value of responsiveness, which we model as the cost premium worth paying to reduce the decision lead time (the justified cost premium). Demand uncertainty arising from jumps rather than from constant volatility increases the justified cost premium when an average jump increases median demand, but decreases the justified cost premium when an average jump decreases median demand. We fit our model to two data sets, first publicly available demand data from Reebok, then point-of-sale data from a supermarket chain. Finally, we present two special cases of the model, one covering a sudden loss of demand, and the other a one-time adjustment to median demand.