The Directive on Adequate Minimum Wages represents a watershed initiative adding substance to the EU's social dimension. It contains two ambitious objectives: establishing the minimum level of statutory minimum wages (SMWs) at 60% of the gross median wage, and increasing collective bargaining coverage (CBC) to at least 80% of workers. In this paper, we assess how minimum wages and collective bargaining affect low pay. Using a time series cross-section of EU-SILC for income years 2004-2019, we identify and assess the absolute and relative size of 'effective wage floors' for full-time employees in 30 countries. We specify multilevel, random effects within-between (REWB) regression models to assess the individual and joint effects of SMW and CBC on wage floors. Our results indicate that SMW and CBC both have distinct roles to play in establishing the effective wage floor. First, countries with a statutory minimum wage have a lower share of workers earning below 60% gross median wage than countries without one. Furthermore, higher rates of CBC are essential for pushing down the share of workers on below-decent pay. Countries without a SMW but with CBC above the 80% target value have roughly the same proportion of below-decent pay as SMW countries with CBC less than 30-40%. However, at higher rates of CBC, SMW countries are predicted to overtake non-SMW countries on this measure. A hypothetical SMW country meeting the target value of 80% CBC is predicted to have less than 6.5% of full-time employees earning below-decent pay.