A comparison was made between Shepard's method (inverse-distance weighting) and collocation (linear filtering) for the purpose of predicting gravity anomalies. Tests were made with actual data from southern California and with simulated data created from buried point masses generated by a random number generator. The autocorrelation functions of the simulated and actual gravity data behaved very much alike. In general, the sophisticated collocation method did produce better results and very good variance estimates, compared with Shepard's method, for simulated data. The advantage was less for actual data. The cost of the better results is the use of more computer time. The most important scientific conclusion of this study is that careful trend removal must be done and an adequate data sample obtained to produce truly optimal results from collocation. The variance estimates are much more sensitive to the form and calibration of the model autocorrelation function than are the prediction results.