A laboratory study examines (a) the effects of source and participant anonymity on the incidence of counter-normative arguments during computer-mediated discussion of an issue that has a normative position, and (b) how the incidence of counter-normative arguments, in turn, affects members' agreement with the normative position. In source-anonymous groups, members know their group's composition but they do not know who has provided what input. In participant-anonymous groups, members do not know their group's composition or the source of any input. When initial opinions among group members differ, source anonymity leads to a lower incidence of counter-normative arguments compared with the identified or participant-anonymity conditions. In groups with a lower incidence of counter-normative arguments, there is greater agreement with the issue's normative position, and members also deviate less from each other after the discussion. Theoretical and practical implications of the results are presented.