The problem discussed is that of measuring a dispersion law from a “stack” of records of surface waves. The method optimally weights different frequencies in the records according to the signal-to-noise ratio as measured from the data and directly estimates coefficients required to complete the specification of a formula giving the dispersion law. The accuracy of the estimates of the dispersion law can be measured and also the homogeneity of the members of the stack can be tested. The method is illustrated on a stack corresponding to seven earthquakes nearly on the great circle joining the World Wide Standard Seismograph Network stations located at Adelaide and Hobart, Australia. The method was originally designed for the case of a stationary signal and noise at the recorders that is incoherent with the signal and between recorders. The stationarity of the signal is not fundamental to the validity of the method but the incoherence assumptions are. Some discussion of this problem is given in the final section of this paper.