In a previous paper, a global optimization algorithm, called MLEW, is provided for finding Maximum Likelihood Estimators for the three-parameter Weibull distribution. A conjecture of Rockette, Antle and Klimko (1974) states that the log-likelihood function of the three-parameter Weibull distribution has never more than two stationary points. Assuming this conjecture to be true, we propose in this paper an improved version of algorithm MLEW, called MLEWh. This last algorithm is heuristic, due to the assumption made, but no sample has been found for which it failed to find a globally optimal solution. Moreover, an extensive empirical comparison is made between algorithms MLEW and MLEWh.