We present results of a detailed simulation study of neutron background reduction in dark matter detectors based on observation of nuclear recoils below 100 keV. Background rates are estimated for neutrons from muons and from natural radioactivity, and with separate Monte Carlo simulations for the underground rock, shielding, and detector components. With optimum shielding combinations, further reduction of background can be achieved with muon and neutron vetos, simulations of the latter giving first estimates of the rejection efficiency as a function of veto geometry. Design options for neutron vetos are also discussed. A detailed tabulation of backgrounds is given, from which it is concluded that the total neutron background can be reduced below the level 10−4–10−3 kg−1 d−1 needed to detect dark matter particle-nucleon cross sections in the range 10−10–10−9 pb, with further reductions attainable in principle with lower-activity detector materials.