Recent work on roll call votes has demonstrated the importance of considering more explicitly the agenda tree that leads to the votes considered. When doing so, the issue of whether members of parliament behave sincerely or in a sophisticated manner comes to the forefront. While a series of studies have, on the basis of examples mostly taken from the US Congress, tried to analyze with the help of theoretical models sophisticated voting, few studies have considered this type of voting in a bicameral setting. The present study proposes a game-theoretic model of sophisticated voting in a bicameral parliament. Assuming incomplete information on the preferences across the two chambers, the analysis demonstrates that in bicameral settings sophisticated voting cannot be considered chamber by chamber, but has to be analyzed in the context of the whole voting process.