The Italian university system has long been characterised by high non-completion rates, though aggregate data show a slight reduction of dropouts in recent years. The most straightforward theoretical explanation for this lies in the lowering opportunity cost of studying due to the financial and economic crisis. Nonetheless, this interpretation is likely to be partly misleading. Indeed, when the crisis hit Italy, enrolment rates had been declining for years and the sample of freshmen has become increasingly selected according to family "social class", family cultural background, type of high school diploma and individual ability. Since a good family background, as well as other individual characteristics, significantly increases students' probability of succeeding, the recent decline in dropout rates could partly depend on sample selection. By applying probit selection models and decomposition techniques to a sample of Italian university students enrolled in different periods of time, I find that changes in students' background and students' characteristics play a major role in the recent reduction of the aggregate dropout rate.