Sorting is a useful predictor for permeability. We show how to invert seismic data for a permeable rock sorting parameter by incorporating a probabilistic rock-physics model with floating grains into a Bayesian seismic inversion code that operates directly on rock-physics variables. The Bayesian prior embeds the coupling between elastic properties, porosity, and the floating-grain sorting parameter. The inversion uses likelihoods based on seismic amplitudes and a forward convolutional model to generate a posterior distribution containing refined estimates of the floating-grain parameter and its uncertainty. The posterior distribution is computed using Markov Chain Monte Carlo methods. The test cases we examine show that significant information about both sorting characteristics and porosity is available from this inversion, even in difficult cases where the contrasts with the bounding lithologies are not strong, provided the signal-to-noise ratio (S/N) of the data is favorable. These test cases show about 25% and 15% improvements in estimated standard deviations for porosity and floating-grain fraction, respectively, for peak S/N of . The full posterior distribution of floating-grain content is more informative, and shows enhanced separation into two clusters of clean and poorly sorted rocks. This holds true even in the more difficult test case we examine, where notably, the laminated reservoir net-to-gross is not significantly improved by the inversion process.