Animals, including humans, learn to discriminate between the diverse sensory stimuli in their environments and to generalize their behaviors to new instances of those stimulus types. For example, rain can sound dramatically different as it falls on different surfaces and yet we have no problem classifying it as rain and discriminating it from speech. While we have some understanding of how generalization is done along a single stimulus dimension, such as sound frequency or light wavelength, natural stimuli are identifiable by a combination of dimensions. To understand perception, measuring the relative contribution of different stimulus dimensions is essential. Do animals discriminate two stimuli to be of different classes, or generalize them into the same class, because of isolated sensory dimensions, or because of their characteristics in some more abstract multi-dimensional space? Is this classification a reflection of the contribution of these dimensions to natural stimuli? We first trained mice to discriminate two sounds that differed in two dimensions, for example frequency range and sweep direction. Then, to test which dimension exerted more behavioral control we measured the generalization of their behavior to novel sounds differing along these two dimensions. We did this across six pairs of auditory dimensions, using an enriched automatic behavioral apparatus where mice live in groups and perform ad libitum. We uncovered a perceptual hierarchy over the tested dimensions. These behavioral results could be explained well by models optimized to represent sound characteristics useful for the prediction or compression of natural sounds, suggesting that the perceptual hierarchy parallels the content of natural stimuli. These results show that perceptual decisions made on complex stimuli involved the integration of different stimulus dimensions according to a hierarchy and that these decisions reflect the relevance of specific stimulus dimensions in the natural world. * on bioRxiv https://www.biorxiv.org/content/10.1101/2021.09.29.462467v1