One popular model of object recognition claims that the visual system typically describes objects using view-specific representations, but that viewpoint-invariant representations are used when objects can be specified uniquely by the arrangement of parts along a single dimension. In a series of three naming experiments using novel, two-dimensional line drawings, we test this hypothesis against alternative accounts of when viewpoint-invariant representations are used during the recognition of upright and viewplane-rotated objects. Experiments 1 and 2 demonstrate that the number of dimensions along which featural information must be represented is the only stimulus feature that influences the type of representation used, consistent with the Tarr and Pinker model. Experiment 3, however, reveals that the use of viewpoint-invariant representations during recognition is not driven purely by stimulus features, and is at least partly under voluntary control. These data suggest that viewpoint-invariant representations are not automatically invoked by the visual system when the requisite stimulus features are present. Rather, our results suggest that top-down control processes, as well as bottom-up stimulus features, jointly determine the conditions under which the visual system uses viewpoint-invariant representations during visual recognition.