This paper introduces certain nonlinear partially observable stochastic optimal control problems which are equivalent to completely observable control problems with finite-dimensional state space. In some cases the optimal control laws are analogous to linear-exponential-quadratic-Gaussian and linear-quadratic-Gaussian tracking problems. The problems discussed allow nonlinearities to enter the unobservable dynamics as gradients of potential functions. The methodology is based on explicit solutions of a modified Duncan-Mortensen-Zakai equation.