Soil compressibility models with physically correct asymptotic void ratios are required to analyze situations that involve a wide stress range. Previously suggested models and other functions are adapted to satisfy asymptotic void ratios at low and high stress levels; all updated models involve four parameters. Compiled consolidation data for remolded and natural clays are used to test the models and to develop correlations between model parameters and index properties. Models can adequately fit soil compression data for a wide range of stresses and soil types; in particular, models that involve the power of the stress σ 0β display higher flexibility to capture the brittle response of some natural soils. The use of a single continuous function avoids numerical discontinuities or the need for ad hoc procedures to determine the yield stress. The tangent stiffness—readily computed for all models—should not be mistaken for the small-strain constant-fabric stiffness.