The effect of enhanced perpendicular diffusion in the polar regions of a simulated heliosphere seems required in drift models for the modulation of galactic cosmic rays in order to find a latitude dependence of cosmic ray protons in the inner heliosphere that is compatible with Ulysses observations. This effect was studied in detail to establish how important it is and to understand the role it plays in global cosmic ray modulation, particularly during minimum modulation periods. After searching through a large parameter space, it was found that enhanced perpendicular diffusion was indeed necessary to obtain compatibility with observations in the inner heliosphere, especially during A>0 magnetic field polarity epochs (e.g., from 1990 to ~2000). This approach, however, also increased the radial dependence during this epoch. Switching to A0 and A<0 solar minimum modulation periods. ¿ 2000 American Geophysical Union