We find the explicit solution to several new problems in stochastic control, among them the finite-fuel problem of optimally tracking a standard Wiener processx+wtstarted atxby a nonanticipating process ξthaving ξ0=0 and total variation (fuel)so as to minimize the expected discounted cost. In n dimensions, the optimal process ξ is given thus: fuel is expended in a singular way to forcex+w–ξtreach and stay in the regionremaining at timet, and f′ is a Bessel (n even) or an elementary function (n odd). Except for a possible initial jump in ξ the processis a degenerate diffusion that reflects at fixed angels off the boundaryand is expressible in terms of the local times on the boundary components.