We model the role of a parliament's structure in shaping the accountability of elected representatives. In a setting in which lawmakers interact with a lobby through a bargaining process and with voters by means of elections, we show that only a single legislative body who can make take it or leave it offers to the lobby can be held unambiguously accountable to voters. Whenever the pressure group enjoys some bargaining power, two chambers might instead provide better discipline, depending on the rules governing their interaction, and in particular the allocation of the decision powers among them. We show that bicameralism with restricted amendment rights provides the best incentives, while unrestricted amendment rights result in a status quo bias. Furthermore, by adding complexity of the legislative process, the presence of a second chamber might lead to an undesirable outcome, i.e. a decline in the legislator's bargaining power vis a vis the lobby and a reduction in his accountability. Arguments suggesting that bicameralism is a panacea against the abuse of power by elected legislators should therefore be taken with due caution.