Europe has over the past century experienced an impressive increase in the number of presidential heads of state. Many of the new democracies since the mid-1970s are semi-presidential regimes that combine a popularly elected president with the traditional features of parliamentary democracy. At the same time, the frequency of the appointment of non-partisan cabinet members has risen. Cabinet appointments are the most important personnel decisions in parliamentary systems, and traditionally such appointments have been virtually monopolized by the governing political parties. Under semi-presidentialism, however, cabinet appointments may instead become a tug-of-war between a prime minister and a president with different partisan preferences. In this article the relationship between presidential power and the incidence of non-partisan cabinet appointments is examined and a game-theoretic model of cabinet appointments in parliamentary systems with a strong president is developed. In this model the prime minister has proposal power over cabinet appointments and the president an ex post veto. This model yields three comparative statics predictions concerning non-partisan cabinet appointments. The incidence of such appointments should covary positively with the president's powers and negatively with the prime minister's electoral prospects. The likelihood of such appointments should also correlate in a non-intuitive way with the value that the president and the prime minister attach to non-partisan appointees. Based on these results, eight operational hypotheses are developed, which are tested against a sample of 134 European cabinets representing twelve semi-presidential and twelve purely parliamentary regimes in the 1990s. Significant empirical support is found for all three comparative statics results and for most of the specific hypotheses.