In recent years, the need for privacy preservation when manipulating or storing personal data, including speech , has become a major issue. In this paper, we present a system addressing the speaker-level anonymization problem. We propose and evaluate a two-stage anonymization pipeline exploiting a state-of-the-art anonymization model described in the Voice Privacy Challenge 2022 in combination with a zero-shot voice conversion architecture able to capture speaker characteristics from a few seconds of speech. We show this architecture can lead to strong privacy preservation while preserving pitch information. Finally, we propose a new compressed metric to evaluate anonymization systems in privacy scenarios with different constraints on privacy and utility.