A multivariable search method is used to predict the optimum design parameters of a gamma-ray scatter gauge for the measurement of the atmospheric density on Mars. The gauge design parameters are incorporated into mathematical models that can be used to calculate the signal and noise responses of the gauge. Then the optimum performance criterion, which consists of the noise-to-signal squared ratio, is minimized by searching these models over the allowable range of values of the gauge design parameters. The optimum values of gamma-ray energy, source-detector distance, and lower- and upper-discriminator settings found in this manner were 106.4 keV, 225 cm, 67.2 keV, and 83.5 keV.