Trust negotiation is a promising approach for establishing trust in open systems, in which sensitive interactions may often occur between entities with no prior knowledge of each other. Although, to date several trust negotiation systems have been proposed, none of them fully address the problem of privacy preservation. Today, privacy is one of the major concerns of users when exchanging information through the Web and thus we believe that trust negotiation systems must effectively address privacy issues in order to be widely applicable. For these reasons, in this paper, we investigate privacy in the context of trust negotiations. We propose a set of privacy-preserving features for inclusion in any trust negotiation system, such as the support for the P3P standard, as well as a number of innovative features, such as a novel format for encoding digital credentials specifically designed for preserving privacy. Further, we present a variety of interoperable strategies to carry on the negotiation with the aim of improving both privacy and efficiency.