A mathematical programming procedure for smoothing coal washability data is presented. The procedure which is derived from classical optimisation theory generates a mathematical program which is solved to provide values of fractional mass and ash percent for a large number of narrow density intervals lying inside the coarser density intervals of the test data. The solution values are constrained to ensure their feasibility and to retain the attributes of the test data. The magnitudes of the narrow density intervals are selected so that the smoothed data can be used directly for data plotting, plant design, equipment performance prediction, optimisation of parallel streams, etc. This procedure offers advantages over the more generally used interpolation methods in that feasible results are guaranteed for ail feasible sets of test data. The paper demonstrates the principal advantage of the.mathematical programming procedure by comparing it with cubic spline interpolation for a set of real but difficult to model washability data.