This paper compares observations of proton distributions made by the Solar Wind Ion Composition Spectrometer (SWICS) ion mass spectrometer on Ulysses at nearly interplanetary shocks with Monte Carlo simulations of particle acceleration at oblique collisionless shocks. The shock parameters are obtained from upstream measurements of the solar wind and magnetic field, and the input particles are drawn from convected Maxwellians, representing solar wind particles. Good agreement between downstream spectral measurements and the simulation predictions are obtained by allowing the parameter lambda/r(sub g), the ratio of the mean-free scattering length to the ionic gyroradius, to vary in an optimization of the fit to the data. Generally lambda/r(sub g) is found to be less than about 20, which corresponds to the case of strong scattering.