High-growth firms contribute disproportionately to the creation of employment, wealth and economic development on a global basis. Yet, knowledge of the circumstances under which such growth patterns occur is limited, and the findings with regard to small and medium sized enterprises (SMEs) are inconclusive. Adopting the behavioural agency model, we analyse the effect of family control and related nuances (i.e. degree of family ownership and presence of a family chief executive officer (CEO)) on SME growth. Furthermore, we argue that the type of slack resources and their availability are a crucial organisational contingency when investigating high growth in SMEs. Using a sample of 39,631 European SMEs over a 13-year period, we find that family firms are less likely to achieve high growth compared to non-family firms; having a family CEO further reduces this likelihood. Instead, at higher (vs lower) levels of family ownership, the probability of family firms achieving high growth increases. Furthermore, the availability of high- and low-discretion slack resources influences these relationships. Our study advances current understanding of high growth in general, and family firms in particular.