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We analyze the performance of a new routing strategy for all-optical packet networks. This strategy improves the Eulerian routing technique, a convergence routing based on a an Eulerian directed cycle. This new technique allows to use shortcuts along the Eulerian cycle. Usual Eulerian routing provides deterministic transport delays but has a very low network utilization. With this new strategy the average transport time is much smaller and we can prove a deterministic upper bound of the transport delay, unlike deflection routing which suffers from livelocks. We study the performance guarantees provided by this new algorithm using graph arguments for the ending property and simulations to give some insights for the performance of the algorithm.