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Vector filters based on order-statistics have proved successful in removing impulsive noise from colour images while preserving edges and fine image details. Among these filters, the ones that involve the cosine distance function (directional filters) have particularly high computational requirements, which limits their use in time-critical applications. In this paper, we introduce two methods to speed up these filters. Experiments on a diverse set of colour images show that the proposed methods provide substantial computational gains without significant loss of accuracy.