Acevedo-Siaca et al. (2021) reported that Amax (at saturating CO2) is more heritable than Asat (at ambient CO2) in rice and suggested the former to be selected to improve photosynthesis under rising ambient [CO2] levels. This commentary hypothesizes sink limitation to be a factor contributing to low genotypic Amax via feedback inhibition (acclimation) of photosynthesis as observed under elevated [CO2]. This process may to some extent also happen under current ambient [CO2]. If confirmed, future breeding for greater photosynthesis should seek improving carbon sink traits as opposed to (or in addition to) modifying the photosynthetic apparatus, which is more difficult.