Using nationally representative panel data on 7,766 individuals (22,878 observations), we investigate the association between several well-being indicators (depression, anxiety, stress, and loneliness) and the general tendency to follow official recommendations regarding selfprotection against COVID-19, in France, Germany, Italy, Spain, and Sweden over the course of four data collection waves. Employing a flexible specification that allows the correlation to be non-monotonic, we find a U-shaped relationship, in which transitions to low and high levels of psychological well-being are associated with higher overall compliance, while transitions to medium levels of psychological well-being are associated with less compliance. Moreover, anxiety, stress, and loneliness levels at baseline also have a U-shaped effect on following the recommendations later (i.e., recommendations are followed best by those with lowest and highest levels of anxiety, stress, and loneliness at baseline, while following the recommendations is lowest for those with moderate levels of these variables). These U shapes are in contrast to previous studies which report monotonic relationships between various measures of mental health and compliance, or ambiguous results. Additionally, we observe a U-shaped correlation between the well-being indicators and a number of specific behaviours (including washing hands and mask wearing). Importantly, most of these specific behaviours play a role in the general tendency to follow recommendations. Finally, we uncover the role of gender composition effects in some of our results. While variations in depression and stress are negatively correlated with variations in overall compliance for males, the association is positive for females. The relation in the full sample (composed of males and females) will reflect first the negative slope for males and then the positive slope for females, explaining the U shape