An understanding of the drivers of tree growth at the species level is required to predict likely changes of carbon stocks and biodiversity when environmental conditions change. Especially in species-rich tropical forests, it is largely unknown how species differ in their response of growth to resource availability and individual size. We use a hierarchical Bayesian approach to quantify the impact of light availability and tree diameter on growth of 274 woody species in a 50-ha long-term forest census plot in Barro Colorado Island, Panama. Light reaching each individual tree was estimated from yearly vertical censuses of canopy density. The hierarchical Bayesian approach allowed accounting for different sources of error, such as negative growth observations, and including rare species correctly weighted by their abundance. All species grew faster at higher light. Exponents of a power function relating growth to light were mostly between 0 and 1. This indicates that nearly all species exhibit a decelerating increase of growth with light. In contrast, estimated growth rates at standardized conditions (5 cm dbh, 5% light) varied over a 9-fold range and reflect strong growth-strategy differentiation between the species. As a consequence, growth rankings of the species at low (2%) and high light (20%) were highly correlated. Rare species tended to grow faster and showed a greater sensitivity to light than abundant species. Overall, tree size was less important for growth than light and about half the species were predicted to grow faster in diameter when bigger or smaller, respectively. Together light availability and tree diameter only explained on average 12% of the variation in growth rates. Thus, other factors such as soil characteristics, herbivory, or pathogens may contribute considerably to shaping tree growth in the tropics.