A technique is described for the optimal synthesis of n-variable combinational logic circuits with Multiplexer universal logic modules, which may readily be implemented without excessive computer storage requirements. The method requires knowledge of the Rademacher-Walsh spectrum, which is an alternative representation of the truthtable vector of the function being considered. It makes use of a property of chosen subsets of these spectra coefficients, which when operated upon can give good indications of the merits of particular decompositions. It is found that an optimal choice of control input variables, and hence aminimal number of multiplexer modules in the realisation, can be made by relatively few tests on the spectral coefficient values.