A key issue in parliamentary democracy centers on the parliament’s ability to contain ministerial drift. Recent scholarship highlights the importance of strong legislative institutions for enforcing the parliament’s wishes, emphasizing that the ministers’ policy choices can often be corrected after the fact by the overseeing standing committees. In this paper, we argue that the parliament’s oversight can also create strong incentives for the ministers to adapt their policy positions in advance—and thereby obviate any need for actual parliamentary enforcement. To substantiate our analysis, we field five decades’ worth of data from the Swedish government and show that the ministers systematically stack their bills in the parliament’s favor already at the agenda-setting stage. Specifically, by selectively eschewing proposals from individual ministers that lie relatively far from the parliament’s ideological position, the ministers collectively ensure that the bulk of bills that reach the parliament will typically support the parliament’s interests. Our conclusions suggest that ministers in parliamentary governments may enjoy significantly less policy discretion than is commonly believed.