The latitudinal gradient of cosmic ray protons observed by Ulysses during September 1994 to July 1995 is small, and it increases as function of rigidity up to ~2 GV and then decreases. Although previous drift models could reproduce the observed small positive gradient for an A>0 solar polarity cycle, they produced a maximum at a rigidity well below 1 GV, in contrast to the observations. After exploring various options, it turns out that changing the rigidity dependence of the perpendicular diffusion coefficient (DC) in the polar direction so that it differs from that of the parallel DC is the most effective way to obtain good agreement with data. Specifically, we find that this DC must have a flatter rigidity dependence than the parallel DC in order to reproduce the observed rigidity dependence of the latitudinal gradient of protons during an A>0 solar polarity cycle. We argue that the present study, combined with studies by other authors, suggests that the perpendicular mean-free path of particles with rigidity R≳0.1 GV has at least two distinct components. One is independent of particle rigidity, and one is proportional to the square of the particle rigidity at low rigidity and flattens to become almost independent of it at higher rigidity. We also show an example of the rigidity dependence of this gradient that Ulysses might observe during an A0 cycle and could impose stricter constraints on the diffusion tensor. ¿ 2000 American Geophysical Union