We use a panel approach, covering 10 EU Member States over the period 1981 to 1999, for each of three major industry groups (manufacturing, construction, and services) and 18 more detailed industries to test whether the EU’s Single Market Programme has led to a reduction in firms’ markups over marginal costs. We address explicitly the uncertainty with respect to the timing of the changeover and allow for a possibly continuous regime shift in a smooth transition analysis. Where regime shifts can be found, the velocity of transition is extremely high, making the linear model a justifiable approximation. We also test for discrete structural breaks in the time window from 1988 to 1996, taking up endogeneity concerns in a GMM framework. Markup reductions are found for aggregate manufacturing (though it is also suggested that markups increased in some manufacturing industries in the pre-completion period at the end of the 1980s) and – less robustly – for construction. In contrast, markups have gone up in most service industries since the early 90s, which confirms the weak state of the Single Market for services and suggests that anti-competitive defense strategies have emerged in the 1990s in service industries.