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This paper considers acoustic inversion for a minimum-structure geoacoustic model in a range-dependent environment. The general survey configuration consists of recording acoustic fields at a vertical array of sensors due to a number of sources distributed in range along a track. The unknown model consists of the sound speeds and thicknesses of sub-bottom layers, which vary with range in an arbitrary manner, and geometric parameters of the experiment. The goal is to determine a range-dependent geoacoustic model with the least structure that is consistent with the resolving power of the data. An under-parametrized approach is developed, which consists of solving the inverse problem a number of times, each time increasing the range variability allowed in the model. The optimal parametrization is subsequently obtained by examining the data mismatch and a norm of the model structure as a function of the number of parameters. The individual inversions are performed using an adaptive hybrid inversion algorithm applied to all data simultaneously.