Most research on anonymity in computer-supported collaborative learning, which has reported both positive and negative outcomes, largely focuses on a fully anonymous login mode. In this context, further research is necessary to finetune the approach to the 'login mode' to optimise the potential benefits while mitigating the drawbacks. This study tests a subtle variation in this mode by which messages remain anonymous to peers (APM) but not to the teacher. We designed a quasi-experimental study with an analysis of the conversations and preferences of first-year university students (N = 109), conducted by employing content analysis of the log data and a post-task questionnaire. We conclude that APM is more productive in terms of participation and discussion oriented to content than in a completely anonymous mode. Additionally, a content analysis of the discussion messages focused on'off task'messages has been performed aiming to enhance comprehension of their nature, impact on social interactions, and the patterns associated with their use. The outcome of this analysis has resulted in a first attempt at a taxonomy that enhances the understanding of the APM and its impact on social interactions in CSCL environments.