Techniques for detection, evaluation, and prediction of pore pressures in low-permeability rocks and equations for fluid-pressure computations in most integrated basin-modeling software are based on relationships between porosity and effective stress in shales. However, recent data show that overpressured shales in the North Sea do not exhibit higher porosities than the normally pressured shales of the same formation at similar depths. To further evaluate the existence of porosity vs. effective stress relationships in shales, fluid-flow simulations and porosity modeling in a typical high-pressure and high-temperature well in the North Sea were undertaken. The parameters in the permeability and porosity equations were adjusted until a satisfactory fit was achieved between the observed and modeled porosity and fluid pressure at present. However, the modeled porosity and pore pressure vs. depth history of the sediments deviated significantly from known porosity and pore pressure vs. depth relationships that have been observed in North Sea shales and elsewhere today. Because the results from basin modeling based on porosity-stress relationships were unacceptable, irrespective of parameter choices, and the well data from the North Sea show no signs of elevated porosities in the overpressured shales, it is inferred that effective stress-driven compaction alone has not generated the hard overpressures observed in deeply buried North Sea shales. These conclusions are suggested to be generally applicable to shales with low porosities and hard overpressures worldwide, both because of the physics involved and because similar results can be extracted from published modeling in the Niger Delta.