The control of organ size presents a fundamental open problem in biology. A declining growth rate is observed in all studied higher animals, and the growth limiting mechanism may therefore be evolutionary conserved. Most studies of organ growth control have been carried out in Drosophila imaginal discs. We have previously shown that the area growth rate in the Drosophila eye primordium declines inversely proportional to the increase in its area, which is consistent with a dilution mechanism for growth control. Here, we show that a dilution mechanism cannot explain growth control in the Drosophila wing disc. We computationally evaluate a range of alternative candidate mechanisms and show that the experimental data can be best explained by a biphasic growth law. However, also logistic growth and an exponentially declining growth rate fit the data very well. The three growth laws correspond to fundamentally different growth mechanisms that we discuss. Since, as we show, a fit to the available experimental growth kinetics is insufficient to define the underlying mechanism of growth control, future experimental studies must focus on the molecular mechanisms to define the mechanism of growth control.