In transportation planning there can be long lead times to adapt capacity. This paper addresses two questions. First, in a one mode world (say rail or road), what is the optimal capacity choice when faced with uncertain demand, long lead times and congestion. Using a simple analytical model it is shown that when demand is inelastic, it is socially optimal to invest more than if only the expected level of demand is taken into account. In this case it may be beneficial to overinvest in capacity because congestion costs are a convex function of relative use. This result holds with or without optimal tolling. The second question deals with two competing modes and where only one mode has long lead times for capacity while the other has flexible capacity. This is typical for the competition between High Speed Rail and air for the medium distance trips (500 to 1000 km), or for the competition between inland waterways and trucks for freight. We find that overinvestment is less justified because the substitute mode can more easily absorb the high demand outcomes.