Single-photon cooling is a recently introduced method to cool atoms and molecules for which standard methods might not be applicable. We numerically examine this method in a two-dimensional wedge trap as well as in a two-dimensional harmonic trap. An element of the method is a small optical box with ``diodic{''} walls which moves slowly through the external potential and catches atoms irreversibly. We show that the cooling efficiency of the method can be improved by optimizing the trajectory of this box.