Does knowing the person who gives you feedback change the way you accept or refuse that feedback? This is the question that motivated our study that compared the effectiveness and perception of anonymous and conference peer feedback on the writing of learners of English as an Additional Language (EAL). This piece of research had 24 participants who attended two classes of EAL at upper-intermediate level in an extension project at a university in Brazil. Both groups were experimental. One group engaged with asynchronous peer feedback via email only, and the other also had a peer conference (face-to-face interaction) after receiving the feedback via email. Data, collected over one semester, encompassed first drafts, peer feedback, and revised drafts of an argumentative essay along with responses to a perception questionnaire. The results showed that both types of feedback were effective to a similar extent, although they differed on how it was processed. While peer conferences were seen as an opportunity for learners to clarify outstanding feedback issues, they did arouse some hostility. Deindividuation, the feeling individuals have when in groups, seemed to foster more feedback among anonymous reviewers. Furthermore, the study found that learners seem to pay more attention to peer feedback than to teacher feedback because of the uncertainty it generates, which might enhance noticing. This uncertainty was perceived as a trigger for further scrutiny and research on the feedback received. Based on the analysis, we argue that there is room for both types of feedback in the EAL classroom. However, the anonymous type, which is the least common, could be an interesting option for developing learners language abilities without the pressure of face-to-face meetings.