This letter proposes a new and comprehensive set of convergence conditions for a distributed optimal traffic engineering method for connectionless networks. The method was originally proposed in, but we show in this letter that the convergence conditions accompanying the method in are not comprehensive and work only in some conditions. More precisely, it is shown that the adaptation laws in will misbehave in some situations. Consequently, they can not achieve optimal resource allocation. This letter presents the correct form of the convergence conditions under which the adaptation laws can effectively lead to optimal network utilization.