Abstract : The concept of a shape index was introduced in Part I to characterize the water retention curve. A potential problem with the parameterization of retention data is the interdependency of parameter values and their conversion to other parametric models. In this Part II the shape index is used to derive formulae for the conversion between: (i) hydraulic parameters of the Brooks-Corey (BC) and van Genuchten (vG) equations, (ii) parameter sets with and without the constraint that the residual water content r = 0, and (iii) vG-shape parameters with different constraints. The dependency of hydraulic parameters on the optimization strategy and the applicability of conversion equations were investigated with 660 retention curves from the GRIZZLY database. The BC-shape parameter and the vG-shape factor mn are poorly correlated for larger and mn (overall r2 = 0.96 for r = 0). Instead of the commonly used equality = mn, conversion based on the shape indices PBC and PvG is more accurate (r2 = 0.99). The shape index is also convenient to accurately predict shape parameters for different constraining scenarios involving r and m = 1 – k/n. The values for r and the shape parameters and mn are not unique. They are positively correlated to maintain the same soil water capacity for a particular soil. For the optimization of parameters, we recommend constraining r. Accurate optimization of retention data, in particular the shape parameters, is possible by constraining r to a non-zero value inferred from the shape index.