Two theoretically derived entropy optimization methods for design of distillation columns with multiple heat exchangers have recently been presented in the literature. These two methods, called equal thermodynamic distance (ETD) and equipartition of forces (EoF), have here been applied to binary distillation and compared. For a 17 plate column separating benzene and toluene the entropy production inside the ETD column was found to be 32.8% less than the comparable adiabatic column while the entropy production in the EoF column was 32.6% less. A numerically calculated optimum was found to be 37.3% better than the adiabatic column. The difference between the EoF column and the numerical optimum occurs mainly in the end sections where the EoF operating line requires driving forces which are difficult to obtain because of the mass balance. The mismatch is mainly due to (i) failure to lake bulk fluxes into account, (ii) mass balance restrictions on the driving force in the upper section, and (iii) uncertainty in the application of the Gibbs-Duhem equation. The ETD column differs from the numerical optimum much in the same manner as the EoF column, by requiring step sizes in the end sections which mass balance only allows at high entropy costs. For very large plate numbers, however, the ETD column is almost in complete agreement with the numerical optimum.