This is a comment on a recent paper by A. Hagberg and D. A. Schult [Chaos 18, 037105 (2008)]. By taking the eigenratio of the Laplacian of an undirected and unweighted network as its synchronizability measure, they proposed a greedy rewiring algorithm for enhancing the synchronizability of the network. The algorithm is not capable of avoiding local minima, and as a consequence, for each initial network, different optimized networks with different synchronizabilities are obtained. Here, we show that by employing a simulated annealing based optimization method, it is possible to further enhance the synchronizability of the network. Moreover, using this approach, the optimized network is not biased by the initial network and regardless of the initial networks, the final optimized networks have similar synchronization properties