Many applications of CSPs require partial solutions to be found before all the information about the problem is available. We examine the case where the future is partially known, and where it is important to make decisions in the present that will be robust in the light of future events. We introduce the branching CSP to model these situations, incorporating some elements of decision theory, and describe an algorithm for its solution that combines forward checking with branch and bound search. We also examine a simple thresholding method which can be used in conjunction with the forward checking algorithm, and we show the trade-off between time and solution quality.