The future prospects of Optical Burst Switching (OBS) networks would greatly benefit, in terms of cost and ease of implementation, from limiting or even avoiding the deployment of wavelength conversion capabilities at the network nodes. This paper proposes a new strategy for minimizing wavelength contention in OBS networks. Simulation results suggest that this strategy can significantly reduce the performance penalty of avoiding wavelength conversion at the network nodes. Moreover, the new strategy is shown to outperform a previously proposed strategy, in some cases by several orders of magnitude, in terms of average burst blocking probability.