An optimal causal message ordering algorithm for asynchronous distributed systems was proposed by Kshemkalyani and Singhal and its optimality was proven theoretically. For a system of n processes, although the space complexity of this algorithm was shown to be O(n/sup 2/) integers, it was expected that the actual space overhead would be much less than n/sup 2/. It is difficult to determine the behavior of this algorithm by a theoretical analysis. We measure the overheads of two different implementations of the optimal causal message ordering algorithm via simulation under a wide range of system conditions. The optimal algorithm is seen to display significantly less message space overhead and log space overhead than the canonical Raynal-Schiper-Toueg algorithm.