The following kind of stochastic control problem is considerd: to minimizeindependent Wiener processes,X0Gaussian random variable independent ofobserved, with all causal functionsutbounded by unity admissible. By using recent comparison theorems for solutions of stochastic differential equations, it is possible to prove that the physically obvious law:is indeed optimal. The same result is established via the classical and the martingale methods of approach to stochastic control. Various generalizations of the above model are also discussed.