In the scenario of the Voice Privacy challenge, anonymization is achieved by converting all utterances from a source speaker to match the same target identity; this identity being randomly selected. In this context, an attacker with maximum knowledge about the anonymization system can not infer the target identity. This article proposed to constrain the target selection to a specific identity, i.e., removing the random selection of identity, to evaluate the extreme threat under a whitebox assessment (the attacker has complete knowledge about the system). Targeting a unique identity also allows us to investigate whether some target's identities are better than others to anonymize a given speaker.