We present AQQUA, a censorship-resistant, private, and auditable payment system built on top of Quisquis. AQQUA supports auditing, while maintaining privacy. It allows users to hold multiple accounts, perform concurrent transactions, and features a non-increasing state. AQQUA achieves auditability by introducing two authorities: one for registration and one for auditing. These authorities cannot censor transactions, thus preserving the decentralized nature of the system. Users create an initial account with the registration authority and then privately transact by using provably unlinkable updates of it. Audits can be voluntarily initiated by the users or requested by the audit authority at any time. Compliance is proved in zero-knowledge against a set of policies which include a maximum limit in the amount sent/received during a time period or in a single transfer, non-participation in a specific transaction or selective disclosure of the value exchanged. To analyze the security of AQQUA we formally define a security model for private and auditable decentralized payment systems. Using this model, we prove that AQQUA satisfies anonymity towards both the public and the auditor, theft prevention, and audit soundness.