Model Predictive Control (MPC) is of interest because it is one of the few control design methods which preserves standard design variables and yet handles constraints. This paper focuses on a stochastic MPC problem with constraints specified in a probabilistic sense. Our aim is to study the incorporation of state estimates into the MPC problem. The original problem could be approximated by a deterministic constrained MPC problem for the conditional mean by absorbing the state estimates’ covariances into the constraints. Our idea is explored in a standard discrete time Linear Quadratic Gaussian problem, and is demonstrated with a simple application in network congestion control.