Scholars have debated extensively the impact of presidential rhetoric on public opinion and congressional behavior, but have largely ignored the determinants of what the president actually says. This inattention is partly the result of the difficulty of acquiring systematic observations of presidential speech crafting. We devise a method of quantifying White House staff influence over the composition of rhetoric that captures the multistage negotiations between the president's speechwriters and his policy advisors and provides a framework for future studies on the determinants of presidential rhetoric. We employ our method to study influence over the writing of President George H. W. Bush's announcement of his veto of a tax bill.