The complex process of surface wave propagation over areas of cohesive sediments has generally been treated by assuming a particular rheological behavior for the mud layer, thereby fixing the description of the mud characteristics into the specification of parameters relevant to the selected rheology. The capability of inverting data to recover these parameters is investigated here. Representing the mud layer as a thin viscous fluid, a nonlinear wavemud interaction model, coupled with a nonlinear optimization technique (LevenbergMarquardt), is used to deduce mud characteristics from estimates of wave energy. A set of numerical tests with a deterministic phase-coherent cnoidal wave are conducted to individually estimate viscosity and mud layer depth (keeping one fixed while estimating the other), and to determine the limits of convergence of the inversion algorithm. It is shown that instances of convergence or nonconvergence can be traced to the shape of the dissipation rate curve as a function of the parameter under consideration as well as the location of the initial guesses of the target parameter along that curve. It is found that the estimation of viscosity is less problematic than the estimation of mud layer depth. Tests with random waves are also performed, using both root-mean-square wave height (representation of wave energy) and wave skewness (representation of nonlinear wave properties) as input for the inversion. The use of random waves appears to ameliorate many of the convergence difficulties encountered with the cnoidal wave tests, while the use of wave skewness, while promising, is somewhat less successful. Finally, the inversion algorithm is tested against laboratory data and the deduction of both mud layer depth and viscosity proceed well. Implications for general mud property deduction are discussed.