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Vehicular ad hoc networks (VANETs) are being designed to improve traffic safety and efficiency. To meet this goal, the messages disseminated in VANETs must be trustworthy. We propose a privacy-preserving system that guarantees message trustworthiness in vehicle-to-vehicle (V2V) communications. Vehicle privacy is provided as long as a vehicle does not attempt to endorse the same message more than once. In spite of a message having been validly endorsed, if it is later found to be false, the system offers the possibility of a posteriori tracing the message generator and its endorsers. Our proposal demonstrates a number of distinctive features. The system is equipped with both a priori and a posteriori countermeasures. The threshold used for a priori endorsement can adaptively change according to the message urgency and traffic context, rather than being preset in the system design stage as in existing schemes. The verification of authenticated V2V messages is accelerated by batch message-processing techniques. Simulation results illustrate that the system maintains its performance under various traffic conditions.