The Monte Carlo technique of simulating diffusive particle acceleration at shocks has made spectral predictions that compare extremely well with particle distributions observed at the quasi-parallel region of the earth's bow shock. The current extension of this work to compare simulation predictions with particle spectra at oblique interplanetary shocks has required the inclusion of significant cross-field diffusion (strong scattering) in the simulation technique, since oblique shocks are intrinsically inefficient in the limit of weak scattering. In this paper, we present results from the method we have developed for the inclusion of cross-field diffusion in our simulations, namely model predictions of particle spectra downstream of oblique subluminal shocks. While the high-energy spectral index is independent of the shock obliquity and the strength of the scattering, the latter is observed to profoundly influence the efficiency of injection of cosmic rays into the acceleration process.