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Contention resolution is a major issue in OBS networks. Several proposals that ensure burst transmissions without losses inside the network have been studied in the literature. Two of these proposals are based on combining a collision-free routing and wavelength assignment scheme with simple contention avoidance/resolution mechanisms. The static approach defines variable offsets and ensures contention avoidance by means of a suitable pre-assignment of offset windows to each communication. The dynamic approach guarantees the successful resolution of all contentions by using a single FDL at each intermediate node. Both proposals are based on giving priority to transmissions coming from the upstream. Hence, when an upstream node misbehaves or changes its transmission traffic pattern, it might delay new burst allocations on downstream nodes, leading to burst losses in the worst case. In this paper we deal with the fairness issue of these proposals. Thus, we introduce simple mechanisms that guarantee the transmission of the committed load for each communication, allowing, at the same time, the dynamic sharing of the spare bandwidth on each wavelength. The proposed mechanisms are analyzed by means of simulation.