Scientists have long struggled to establish how larger brains translate into higher cognitive performance across species. While absolute brain size often yields high predictive power of performance, its positive correlation with body size warrants some level of correction. It is expected that larger brains are needed to control larger bodies without any changes in cognitive performance. Potentially, the mean value of intraspecific brain-body slopes provides the best available estimate for an interspecific correction factor. For example, in primates, including humans, an increase in body size translates into an increase in brain size without changes in cognitive performance. Here, we provide the first evaluation of this hypothesis for another clade, teleost fishes. First, we obtained a mean intraspecific brain-body regression slope of 0.46 (albeit with a relatively large range of 0.26-0.79) from a dataset of 51 species, with at least 10 wild adult specimens per species. This mean intraspecific slope value (0.46) is similar to that of the encephalisation quotient reported for teleosts (0.5), which can be used to predict mean cognitive performance in fishes. Importantly, such a mean value (0.46) is much higher than in endothermic vertebrate species (<= 0.3). Second, we used wild-caught adult cleaner fish Labroides dimidiatus as a case study to test whether variation in individual cognitive performance can be explained by body size. We first obtained the brain-body regression slope for this species from two different datasets, which gave slope values of 0.58 (MRI scan data) and 0.47 (dissection data). Then, we used another dataset involving 69 adult cleaners different from those tested for their brain-body slope. We found that cognitive performance from four different tasks that estimated their learning, numerical, and inhibitory control abilities was not significantly associated with body size. These results suggest that the intraspecific brain-body slope captures cognitive equivalence for this species. That is, individuals that are on the brain-body regression line are cognitively equal. While rather preliminary, our results suggest that fish and mammalian brain organisations are fundamentally different, resulting in different intra- and interspecific slopes of cognitive equivalence.