Classical trajectories are calculated on model designed to reproduce the reactive-unreactive bands found with the SSMK and Yates-Lester surfaces for the H + H2 system and other A + BC systems. The model surfaces are based on a rectilinear reaction path, with a constant period of vibration, and have an exit region corresponding to reaction. A simple surface obtained by taking a cut at constant RBC though a collinear potential-energy function is not as satisfactory as one to which a platform has been added to allow for the zero-point energy normal to the minimum reaction path. General principles are derived for obtaining reaction probabilities and reactive-unreactive boundaries for such surfaces. The model surfaces predict the bands in a general way, and throw light on the reason they occur, but do not lead to quantitative predictions.