Pumping of an unconfined aquifer causes local desaturation and a decrease in mass that is proportional to the volume of water drained from the unsaturated pore space assuming small aquifer compressibility.  Under some conditions, ground-based gravity meters can measure the small changes in gravitational acceleration (or gravity) caused by this change in subsurface mass.  Conditions conducive to making these measurements depend on a sufficiently large gravity signal which is primarily influenced by the drainable porosity of the aquifer, the depth to the water table, and distance from the pumping well to the measurement location.  Numerical experiments were conducted to examine the value of drawdown and gravity responses for constraining aquifer test analyses based on synthetic measurements at nine ground-surface locations after seven days of pumping.  Equivalent signal to noise ratios were employed to compare estimates of hydraulic conductivity and specific yield parameters based on drawdown and gravity measurements, both individually and jointly.  Parameter estimates based on drawdown data alone resulted in inaccurate and imprecise estimates of specific yield.  Use of gravity data alone resulted in inaccurate and imprecise estimates of both parameters.  Combined use of drawdown and gravity data resulted in unbiased and precise estimates of both parameters.  This suggests that gravimetry may provide information about the specific yield of an aquifer, which can be difficult to accurately determine with standard hydraulic testing methods.  The inference of hydraulic properties requires consideration of parameter interaction and parameter sensitivity to instrument responses in addition to instrument resolution and signal detectability.  The optimal weighting of the gravity and drawdown information in a single objective function was not consistent with measurement errors.  Rather, the weights on the gravity data were reduced for optimal parameter estimation, likely reflecting parameter interactions due to the distributed spatial sensitivity of gravity measurements.