We discuss the physics of charged-particle acceleration at nearly perpendicular shocks focusing on the limit of weak pitch-angle scattering. Recent observations of large anisotropics of energetic particles upstream of the solar-wind termination shock suggest the particles are very weakly scattered. This raises questions about how rapidly the particles are accelerated by the shock, and whether there is a significant injection problem. We perform new numerical simulations of test protons accelerated by a synthesized termination shock. In our model, the turbulent magnetic field is generated by summing over a large number of discrete plane waves with amplitudes determined from a specified power spectrum and random phases and propagation directions. We study the effect of removing magnetic fluctuations with scales that resonate with the particles in order to model the case where the scattering is very weak (long parallel mean-free paths). Field-line meandering, which we have previously found to be important at quasi-perpendicular shocks, is included. The results are discussed in the context of the Voyagers observations as well as fundamental theory of diffusive shock acceleration. Our primary conclusion is that by removing the short wavelength magnetic fluctuations the efficiency of particle acceleration at the shock is greatly reduced.