Pluto has a heterogeneous surface, despite a global haze deposition rate of ~1 micrometer per orbit (Cheng et al., 2017; Grundy et al., 2018). While there could be spatial variation in the deposition rate, this has not yet been rigorously quantified, and naively the haze should coat the surface more uniformly than was observed. One way (among many) to explain this contradiction is for atmospheric pressure at the surface to drop low enough to interrupt haze production and stop the deposition of particles onto part of the surface, driving heterogeneity. If the surface pressure drops to less than 10^-3 - 10^-4 microbar and the CH4 mixing ratio remains nearly constant at the observed 2015 value, the atmosphere becomes transparent to ultraviolet radiation (Young et al., 2018), which would shut off haze production at its source. If the surface pressure falls below 0.06 microbar, the atmosphere ceases to be global, and instead is localized over only the warmest part of the surface, restricting the location of deposition (Spencer et al., 1997). In Plutos current atmosphere, haze monomers collect together into aggregate particles at beginning at 0.5 microbar; if the surface pressure falls below this limit, the appearance of particles deposited at different times of year and in different locations could be different. We use VT3D, an energy balance model (Young, 2017), to model the surface pressure on Pluto in current and past orbital configurations for four possible static N2 ice distributions: the observed northern hemisphere distribution with (1) a bare southern hemisphere, (2) a south polar cap, (3) a southern zonal band, and finally (4) a distribution that is bare everywhere except inside the boundary of Sputnik Planitia. We also present a sensitivity study showing the effect of mobile N2 ice...(cont.)