The paper introduces a peer-to-peer system called P2PRIV (peer-to-peer direct and anonymous distribution overlay). Basic novel features of P2PRIV are: (i) a peer-to-peer parallel content exchange architecture, and (ii) separation of the anonymization process from the transport function. These features allow a considerable saving of service time while preserving high degree of anonymity. In the paper we evaluate anonymity measures of P2PRIV (using a normalized entropy measurement model) as well as its traffic measures (including service time and network dynamics), and compare anonymity and traffic performance of P2PRIV with a well known system called CROWDS.