A method is provided for safeguarding anonymity during a communication with a correspondent, between a caller and a user being called. The communication has an anonymous nature. The method includes the following steps: upon receiving a response from the correspondent to the communication sent by the caller, putting the caller on hold; analysis of the response received from the correspondent, for determining whether the correspondent corresponds to the voicemail of the user being called; and in the case of a positive determination, playing to the caller an anonymous welcome message in which the identity of the user being called is masked.