An improved analytic solution is presented that describes the dissipation of abnormal pressures via Darcy flow out of a compartment formed of high-permeability rock capped top and bottom by lower permeability rock. The solution tends to the solutions presented by previous workers in the limit of (1) a thick compartment and thin barrier and (2) a thick barrier and a thin compartment. The importance of including fluid compressibility when analyzing hydrocarbon reservoirs is demonstrated. Previous workers in this field have only included the effect of bulk rock compressibility and have neglected fluid compressibility. The solution is applied to pressure compartments on the scale of a typical hydrocarbon reservoir and overpressured regions on the basin scale. It is shown that the pressure gradient in a typical hydrocarbon reservoir compartment will return to the hydrostatic gradient over timescales of the order of hours or days, but that abnormal pressures are likely to dissipate over periods of tens of thousands to hundreds of thousands of years. Thus, any reservoir compartment with a different pressure from its neighbors at discovery can be considered as an independent unit during production. However, abnormal pressures on the basin scale may take tens or hundreds of millions of years to dissipate. There is thus no need to invoke zero-permeability seals or capillary-pressure seals in order to explain the existence of abnormal pressures over geological time.