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Many animals can modify the environments in which they live, thereby changing the selection pressures they experience. A common example of such niche construction is the use, creation or modification of environmental resources for use as nests or shelters. Because these resources often have correlated structural elements, it can be difficult to disentangle the relative contribution of these elements to resource choice, and the preference functions underlying niche-construction behaviour remain hidden. Here, we present an experimental paradigm that uses 3D scanning, modelling and printing to create replicas of structures that differ with respect to key structural attributes. We show that a niche-constructing, shell-dwelling cichlid fish, Neolamprologus multifasciatus , has strong open-ended preference functions for exaggerated shell replicas. Fish preferred shells that were fully intact and either enlarged, lengthened or had widened apertures. Shell intactness was the most important structural attribute, followed by shell length, then aperture width. We disentangle the relative roles of different shell attributes, which are tightly correlated in the wild, but nevertheless differentially influence shelter choice and therefore niche construction in this species. We highlight the broad utility of our approach when compared with more traditional methods (e.g. two-choice tasks) for studying animal decision-making in a range of contexts.