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Inverse hydrologic analysis of compaction-driven groundwater flow provides insights to the distribution and origin of geopressured zones in subsiding sedimentary basins, such as those found in the U.S. Gulf Coast. Occurrences of Gulf Coast-type geopressures are most frequently attributed to “disequilibrium compaction” caused by slow rates of fluid escape from compacting sediments, “aquathermal pressuring” from thermal expansion of pore fluids, or the subsurface dehydration of smectite. This paper presents an inverse solution to the Lagrangian equation of compaction flow that includes effects of aquathermal pressuring and dehydration reactions. The solution gives the permeability profile required to maintain a lithostatic pressure gradient in a subsiding basin. Comparison of the closed-form solution with measured permeabilities shows that geopressured zones are likely to form in shaly basins subsiding more than about 1 mm/yr but unlikely to develop in shale-poor basins or basins subsiding less than 0.1 mm/yr. This result correctly predicts geopressures in the Gulf Coast but suggests that many important sedimentary basins were not significantly overpressured during compaction. Solutions that consider only thermal expansion of pore fluids give required permeabilities about 1.3–1.8 orders of magnitude (factor of 20–60) less than those considering only sediment compaction, indicating that aquathermal pressuring is much less important than disequilibrium compaction in causing geopressures. Solutions accounting for the effects of dehydration reactions show that release of structural water during smectite dehydration can be a significant and perhaps necessary factor in geopressuring. Hydrologic effects of a possible increase in the volume of structural water during dehydration are less significant. The most important contribution of smectite dehydration to development of geopressured zones, however, may be the accompanying reduction of host rock permeability.