Recently in vision science there has been great interest in understanding the perceptual representations of complex multidimensional stimuli. Therefore, it is becoming very important to develop methods for performing psychophysical experiments with multidimensional stimuli and efficiently estimating psychometric models that have multiple free parameters. In this methodological study, I analyze three efficient implementations of the popular Ψ method for adaptive data collection, two of which are novel approaches to psychophysical experiments. Although the standard implementation of the Ψ procedure is intractable in higher dimensions, I demonstrate that my implementations generalize well to complex psychometric models defined in multidimensional stimulus spaces and can be implemented very efficiently on standard laboratory computers. I show that my implementations may be of particular use for experiments studying how subjects combine multiple cues to estimate sensory quantities. I discuss strategies for speeding up experiments and suggest directions for future research in this rapidly growing area at the intersection of cognitive science, neuroscience, and machine learning.