The problem of smoothing dry weather inflow variations for a Waste Water Treatment Plant (WWTP) that receives sewage from multiple mixed sewer systems is formulated. A first rough control algorithm that uses branch and bound is presented. The control algorithm uses a form of Model Predictive Control. Trials showed that the algorithm had trouble satisfying two constraints that were initially regarded as ‘soft’ constraints. As a result, a closer look was taken at the feasibility of the problem. A family of simpler problems were derived to do so. These auxiliary problems made it possible to show that for a given subclass feasibility was strongly dependent on the choice of problem parameters.