This article illustrates how voting rules used to pass a piece of legislation and the structure of the legislation, in terms of whether or not it has single or multiple issue dimensions, influence the frequency and the purpose of position changes in legislative negotiations. Through analysis of data on a set of legislative proposals negotiated in the European Union, I show that position changes are less common under unanimity rule than under majority rule. More importantly, I argue and show that when the negotiated legislation is multidimensional (i.e., contains multiple issues) and the voting rule is unanimity, position changing is a lucrative strategy for legislators. Multidimensional legislation creates opportunities for logrolling, and legislators’ veto power under the unanimity rule enables them to exploit these opportunities. Accordingly, under this scenario, legislators often engage in what I call a within-legislation logroll and secure favorable legislative outcomes.