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The analysis of a bi-dimensional dynamic routing model for alternative routing telecommunication networks led to the identification of an instability problem in the synchronous path selection associated with the complex interdependencies among the coefficients of the objective functions and the computed paths for every node pair. In this paper an analytical model enabling to make explicit this problem and evaluate its effects in terms of two global network criteria, is presented. Also a heuristic procedure dedicated to overcome this instability problem and select “good” compromise solutions in terms of network performance is developed. Finally the performance of the proposed routing method using the heuristic is compared by recurring to discrete-event simulation with a reference dynamic routing method (Real Time Network Routing) for some test networks.