A theoretical analysis is presented that suggests that dispersive pressure in a grain flow, modified grain flow, or traction carpet cannot account for the upward segregation of large particles, as sometimes assumed. The analysis shows that rapid granular flows are self-organized in such a way that dispersive pressure at any level in a shearing mass of grains is always equal to the applied normal stress. An increase in dispersive pressure causes an immediate expansion of the flow and a consequent decrease in dispersive pressure until it equals the applied normal stress again. The gradient of dispersive pressure is therefore "hydrostatic," and only particles lighter than the bulk density of the flow are pushed upward. The inverse grading of heavy particles observed in a great variety of deposits is not caused by dispersive pressure and must be explained by other mechanisms.