Traffic scene analysis is important for emerging technologies such as smart traffic management and autonomous vehicles. However, such analysis also poses potential privacy threats. For example, a system that can recognize license plates may construct patterns of behavior of the corresponding vehicles' owners and use that for various illegal purposes. In this paper we present a system that enables traffic scene analysis while at the same time preserving license plate privacy. The system is based on a multi-task model whose latent space is selectively compressed depending on the amount of information the specific features carry about analysis tasks and private information. Effectiveness of the proposed method is illustrated by experiments on the Cityscapes dataset, for which we also provide license plate annotations.