Describing diffraction of atomic and molecular projectiles at fast grazing incidence presents a real challenge for quantum theoretical simulations due to the high incidence energy (100eV–1keV) used in experiments. This is one of the main reasons why most theoretical simulations performed to date are based on reduced dimensional models. Here we analyze two alternatives to reduce the computational effort, while preserving the real dimensionality of the system. First, we show that grazing incidence conditions are already fulfilled for incidence angles ⩽5°, i.e., incidence angles higher than those typically used in experiments. Thus, accurate comparisons with experiment can be performed considering diffraction at grazing incidence, but with smaller total incidence energies, whilst keeping the same experimental normal energy in the calculations. Second, we show that diffraction probabilities obtained at fast grazing incidence are fairly well reproduced by simulations performed at slow normal incidence. This latter approach would allow one to simulate several experimental spectra, measured at the same normal incidence energy for several incidence crystallographic directions, with only one calculation. This approach requires to keep the full dimensionality of the system.