Pseudonym change schemes have been studied in VANETs to guarantee the property of untraceability of the vehicles. This paper proposes a new condition based on the assumption that if there are no malicious vehicles around when a synchronous change triggers, there is no risk of tracking, and the pseudonym change defers until a time threshold. Thus, our proposal based on a synchronous strategy to increase the anonymity set, adds to the change condition, the checking of the reputation status of the neighbouring vehicles. The reputation status is the result of discretizing the reputation score of the vehicles and it is part of the periodically broadcast beacon messages. The proposal was evaluated through simulations using a real scenario. The results showed an optimization in the use of pseudonyms maintaining similar anonymity levels with other schemes.