In a magnitude estimation experiment, twenty observers rated the brightness of several unrelated, self-luminous stimuli surrounded by a dark background. The performance of a number of existing vision models, color appearance models and models based on the concept of equivalent luminance in predicting brightness has been investigated. Due to a severe underestimation of the Helmholtz-Kohlrausch effect, none of the models performed acceptable. Increasing the weight of the colorfulness contribution to the brightness attribute in the CAM97u model results in a very good correlation between the model predictions and the visually perceived brightness. Finally the experimental results and the brightness prediction from the modified model CAM97u,m are verified through a matching experiment and a validation magnitude estimation experiment.