We present a intuitive and self-contained formulation of a stability preserving receding horizon control strategy for a system where limited preview information is available for the disturbances. The simplicity of the derivation is due to (and its benefits somewhat offset by) a set of stringent and highly structured assumptions. The formulation uses a suboptimal value function for terminal cost, and relies on optimization strategies that only require a trivial improvement property, allowing implementation as an "anytime" algorithm. The nature of this strategy's performance is clarified with linear examples.