A velocity gradient model parameterized with the tau-zeta inversion for seismic refraction data is examined with respect to a synthetic traveltime data set. The velocity-depth model consists of a stack of laterally homogeneous layers, each with a constant velocity gradient. The free model parameters are the velocities of the layer bounds and the number of layers.The best velocity gradient solutions, i.e., with the least deviation from the true model, were obtained from 'constrained' models in which the velocities of the layer bounds are the velocities of the observed refracted waves. An arbitrary selection of layer bound velocities was found to be a suboptimal choice of model parameterization for the tau-zeta inversion.A trade-off curve between model resolution and solution variance was constructed with the constrained model parameterization from examination of numerous solutions with a diverse number of layers. A constrained model with as many layers as observed data points represents a satisfactory compromise between model resolution and solution variance. Constrained models with more layers than observed data points, however, can increase the resolution of the velocity gradient model. If model resolution is favored over solution variance, a constrained model with many more layers than observed data points is therefore the best model parameterization with the tau-zeta inversion technique.