Recent advances in computational models in vision science have considerably furthered our understanding of human visual perception. At the same time, rapid advances in convolutional deep neural networks (DNNs) have resulted in computer vision models of object recognition which, for the first time, rival human object recognition. Furthermore, it has been suggested that DNNs may not only be successful models for computer vision, but may also be good computational models of the monkey and human visual systems. The advances in computational models in both vision science and computer vision pose two challenges in two different and independent domains: First, because the latest computational models have much higher predictive accuracy, and competing models may make similar predictions, we require more human data to be able to statistically distinguish between different models. Thus we would like to have methods to acquire trustworthy human behavioural data fast and easy. Second, we need challenging experiments to ascertain whether models show similar input-output behaviour only near “ceiling” performance, or whether their performance degrades similar to human performance: only then do we have strong evidence that models and human observers may be using similar features and processing strategies. In this paper we address both challenges.