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Within the European Defence Agency (EDA) project Rumble-2, an operational low-frequency active sonar system has been used to collect reverberation data at several sea trials in the North Sea. A global optimization method is used to determine the bottom parameters that provide the best match between measured and modeled time traces. A fast ray model is used for the forward computations. The bottom parameters are the Lambert back-scattering parameter and the sound speed c, density ρ, absorption α, and thickness of the sediment. The reverberation data do not constrain all these parameters to unique values, however, and different approaches have been tried in the project to reduce the ambiguity problems. The approach reported here is to use the mean grain size Mz as a common descriptive parameter. From regression relations by Hamilton and Bachman, c, ρ, and α can be set as functions of Mz. More ambitiously, the regression relations could be applied as a priori constraints, with uncertainties, in a Bayesian framework. The obtained inversion results are consistent with ground truth for the grain size, as measured from bottom samples. Moreover, similar results are obtained for trials in the same area with quite different environmental conditions.