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We present a model for operational stochastic short-term hydropower scheduling, taking into account the uncertainty in future prices and inflow, and illustrate how the benefits of using a stochastic rather than a deterministic model can be quantified. The solution method is based on stochastic successive linear programming. The proposed method is tested against the solution of the true non-linear problem in a principal setting. We demonstrate that the applied methodology is a first-order approximation to a formal correct head-of-water optimization and achieve good results in tests. How the concept of stochastic successive linear programming has been implemented in a prototype software for operational short-term hydropower scheduling is also presented, and the model's ability is demonstrated through case studies from Norwegian power industry. From these studies, improvements occurred in terms of the objective function value and decreased risk of spill from reservoirs.