The deconvolution process is widely used to enhance seismic data by suppressing distortions of the shot pulse caused by such things as reverberations and ghosts. The process consists of estimating the correlation function from the data, determining the inverse filter using the Levinson algorithm, and applying the inverse filter to the data.This paper is concerned with the estimation problem. Certain conclusions about the estimation problem are suggested by the theory of power spectra developed by Tukey and others. By means of a Monte Carlo simulation of the deconvolution process, we have tested these conclusions:(1) Severely distorted data should be prewhitened.(2) Truncators (lag windows) with the same number of degrees of freedom yield the same error.(3) There is an optimum number of degrees of freedom for a fixed data window.(4) Due to time variance in the data, there is an optimum length of data window.Monte Carlo simulation can be used to estimate the optimum values (3) and (4) and so improve the performance of the deconvolution process.