In pore pressure estimation and in basin modelling programs it is often assumed that porosity in clay-rich sediments depends on the vertical effective stress. An alternative assumption is that porosity depends on the mean effective stress. Yet triaxial test data on natural clays have shown that porosity depends on both the mean effective stress and the differential stress. Triaxial test data for Winnipeg clay are re-plotted here to quantify the errors in estimated pore pressures that would result if it is assumed that porosity depends on either vertical or mean effective stress. The assumption that porosity depends on vertical effective stress may result in gross underestimates of pore pressures in compressional basins, where horizontal stresses in overpressured zones at depth are greater than the vertical stress. Sections through the yield surface of Winnipeg clay are consistent with a generalized yield locus for clays, normalized for composition as well as volume, based on data from several natural clays. Consequently, a refined equivalent depth method of pore pressure estimation that accounts for porosity dependence on both mean and effective stress could, in principle, be implemented. The method would require some knowledge of yield properties and of all three principal stresses in the subsurface.