The Efficient Détermination Criterion (EDC) generalizes the AIC and BIC criteria and provides a class of consistent estimators for the order of a Markov chain. Several authors hâve addressed the question of choosing between AIC or BIC estimâtes. The first tends to overestimate the order and the second, though consistent, may lead to underestimation. Ail these estimators are based on penalized maximum log-likelihood functions. In this work, we study the choice of the optimal penalty term and show that corresponds to neither AIC nor BIC estimators.