Hydrographic data, be it raw or highly averaged observational data, contain substantial regions having vertical density inversions. An algorithm is described that minimally modifies such data so that the resulting hydrographic casts have vertical buoyancy frequency profiles larger than a specified lower bound. The method underlying the algorithm is based on the solution of a constrained weighted least-squares problem and maximizes the smoothness of the resulting salinity-potential temperature diagram. Examples are provided that demonstrate the effectiveness of the technique in minimally altering hydrographic data only in the immediate vicinity of the data that do not already satisfy the buoyancy frequency constraint. A modified equation of state, identical in form to the international equation of state of seawater but written in terms of potential rather than in situ temperature, is also provided, enabling rapid computation of the thermal expansion and saline contraction coefficients. Abstract Hydrographic data, be it raw or highly averaged observational data, contain substantial regions having vertical density inversions. An algorithm is described that minimally modifies such data so that the resulting hydrographic casts have vertical buoyancy frequency profiles larger than a specified lower bound. The method underlying the algorithm is based on the solution of a constrained weighted least-squares problem and maximizes the smoothness of the resulting salinity-potential temperature diagram. Examples are provided that demonstrate the effectiveness of the technique in minimally altering hydrographic data only in the immediate vicinity of the data that do not already satisfy the buoyancy frequency constraint. A modified equation of state, identical in form to the international equation of state of seawater but written in terms of potential rather than in situ temperature, is also provided, enabling rapid computation of the thermal expansion and saline contraction coefficients.