The axial dispersion model of hepatic drug elimination is characterized by two dimensionless parameters, the dispersion number, DN, and the efficiency number, RN, corresponding to the relative dispersion of material on transit through the organ and the relative efficiency of elimination of drug by the organ, respectively. Optimal design theory was applied to the estimation of these two parameters based on changes in availability (F) of drug at steady state for the closed boundary condition model, with particular attention to variations in the fraction of drug unbound in the perfusate (fuB). Sensitivity analysis indicates that precision in parameter estimation is greatest when F is low and that correlation between RN and DN is high, which is desirable for parameter estimation, when DN lies between 0.1 and 100. Optimal design points were obtained using D-optimization, taking into account the error variance model. If the error variance model is unknown, it is shown that choosing Poisson error model is reasonable. Furthermore, although not optimal, geometric spacing of fuB values is often reasonable and definitively superior to a uniform spacing strategy. In practice, the range of fuB available for selection may be limited by such practical considerations as assay sensitivity and acceptable concentration range of binding protein. Notwithstanding, optimal design theory provides a rational approach to precise parameter estimation.