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Vehicular ad hoc networks (VANETs) allow vehicle-to-vehicle communication and, in particular, vehicle-generated announcements. Provided that the trustworthiness of such announcements can be guaranteed, they can greatly increase the safety of driving. A new system for vehicle-generated announcements is presented that is secure against external and internal attackers attempting to send fake messages. Internal attacks are thwarted by using an endorsement mechanism based on threshold signatures. Our system outperforms previous proposals in message length and computational cost. Three different privacy-preserving variants of the system are also described to ensure that vehicles volunteering to generate and/or endorse trustworthy announcements do not have to sacrifice their privacy.