Sandstone pressures follow the hydrostatic gradient in Miocene strata of the Mad Dog field, deep-water Gulf of Mexico, whereas pore pressures in the adjacent mudstones track a trend from well to well that can be approximated by the total vertical stress gradient. The sandstone pressures within these strata are everywhere less than the bounding mudstone pore pressures, and the difference between them is proportional to the total vertical stress. The mudstone pressure is predicted from its porosity with an exponential porosity-versus-vertical effective stress relationship, where porosity is interpreted from wireline velocity. Sonic velocities in mudstones bounding the regional sandstones fall within a narrow range throughout the field from which we interpret their vertical effective stresses can be approximated as constant. We show how to predict sandstone and mudstone pore pressure in any offset well at Mad Dog given knowledge of the local total vertical stress. At Mad Dog, the approach is complicated by the extraordinary lateral changes in total vertical stress that are caused by changing bathymetry and the presence or absence of salt. A similar approach can be used in other subsalt fields. We suggest that pore pressures within mudstones can be systematically different from those of the nearby sandstones, and that this difference can be predicted. Well programs must ensure that the borehole pressure is not too low, which results in borehole closure in the mudstone intervals, and not too high, which can result in lost circulation to the reservoir intervals.