Can men and women have equal levels of voice and authority in deliberation or does deliberation exacerbate gender inequality? Does increasing women's descriptive representation in deliberation increase their voice and authority? We answer these questions and move beyond the debate by hypothesizing that the group's gender composition interacts with its decision rule to exacerbate or erase the inequalities. We test this hypothesis and various alternatives, using experimental data with many groups and links between individuals' attitudes and speech. We find a substantial gender gap in voice and authority, but as hypothesized, it disappears under unanimous rule and few women, or under majority rule and many women. Deliberative design can avoid inequality by fitting institutional procedure to the social context of the situation.