A new method of estimating pharmacokinetic parameters for enterohepatic recirculation models is presented. The algorithm, based on the simplex method, assures a convergence toward the minimum minimorum; provides reliable parameters, even in large numbers; and handles up to five cycle effects in five established models: IV, EV, mono-, bi- or tricompartmental. For each model, the reabsorption rate may be considered to be slow (characterised by a rate constant with a significant value) or instantaneous (an infinite rate constant). Two examples are given to illustrate the qualities of the software that incorporates this new algorithm. The first relates to the pharmacokinetics of zinc orally given to humans; the second treats the kinetics of alpha-methylDOPA given to dogs intra-arterially (note: values of plasma concentrations have been extracted from the literature).