Training experiments were performed to investigate the ability of goldfish to discriminate objects differing in spatial depth. Tests on size constancy should give insight into the mechanisms of distance estimation. Goldfish were successfully trained to discriminate between two black disk stimuli of equal size but different distance from the tank wall. Each stimulus was presented in a white tube so that the fish could see only one stimulus at a time. For each of eight training stimulus distances, the just noticeable difference in distance was determined at a threshold criterion of 70% choice frequency. The ratio of the retinal image sizes between training stimulus and comparison stimulus at threshold was about constant. However, in contrast to Douglas et al. (Behav Brain Res 30:37-42, 1988), goldfish did not show size constancy in tests with stimuli of the same visual angle. This indicates that they did not estimate distance, but simply compared the retinal images under our experimental conditions. We did not find any indication for the use of accommodation as a depth cue. A patterned background at the rear end of the tubes did not have any effect, which, however, does not exclude the possibility that motion parallax is used as a depth cue under natural conditions.