Most experiments on conformity have been conducted in relation to judgments of physical reality; surprisingly few papers have experimentally examined the influence of group norms on social issues with a moral component. In response to this, participants were told that they were either in a minority or in a majority relative to their university group in terms of their attitudes toward recognition of gay couples in law (Expt 1: N = 205) and a government apology to Aborigines (Expt 2: N = 110). In both experiments, it was found that participants who had a weak moral basis for their attitude conformed to the group norm on private behaviours. In contrast, those who had a strong moral basis for their attitude showed non-conformity on private behaviours and counter-conformity on public behaviours. Incidences of non-conformity and counter-conformity are discussed with reference to theory and research on normative influence.