In cooperative localization, target users take advantage of neighboring users in the network to improve their position estimates. In dense networks, the number of neighbors is high and consequently a very large amount of information is available. Using all neighbors (full cooperation) results in a considerable amount of data that is to be processed and transmitted causing high network traffic, delays and reduced battery lifetime. The goal in censoring is to limit the amount of cooperation to reduce the amount of data to be transmitted, without losing (much) in positioning accuracy compared to full cooperative localization. In this paper we propose a novel censoring technique based on the Bayesian Cramer-Rao Lower Bound (CRLB) that takes into account both the uncertainties of the neighbors and the link quality in terms of LOS/NLOS. With the use of the unscented transform and a greedy search approach, the censoring can be performed accurately and at a low computational complexity.