Fast-growing cyanobacterial and microalgal strains are considered to be a promising resource to overcome current productivity barriers of phototrophic cultivation. The purpose of this communication, however, is to argue that a high maximal growth rate itself is not a sufficient or necessary property for high phototrophic productivity. Rather, the light-limited specific growth rate of a phototrophic microorganism is a product of several factors, including the rate of light absorption, the photosynthetic efficiency, and the maximal biomass yield per mol photons. It is suggested that, in addition to the maximal growth rate, reports on fast-growing strains should also assess photosynthetic efficiency and maximal biomass yield as predictors of culture productivity. The arguments within the communication are underpinned by a theoretical analysis of a light-limited chemostat, compared to its heterotrophic counterpart. It is shown that for the light-limited chemostat maximal productivity occurs at low dilution rates.