A series of speeded classification tasks proposed by Garner (1974) has become a well-entrenched method for identifying interactions between perceptual dimensions. The theory proposes that integral dimensions should produce a redundancy gain when a second dimension covaries perfectly with the attended dimension, and interference if the second dimension varies irrelevantly. This work questions the interpretation of such results as indicating interactive dimensions, reviewing independent models which naturally exhibit such effects. Furthermore, there are several methodological confounds which make the cause of Garner interference non-identifiable in the standard experimental context, the most serious of which is the conflation of changes in the number of stimuli with changes in the number of irrelevant dimensions. Here is proposed a novel three-dimensional extension of the Garner paradigm capable of disambiguating these experimental factors, which includes several conditions designed to help distinguish between various competing models of the related phenomena. This new paradigm was implemented with two stimulus sets, both composed of known integral dimensions, but from opposite sides of the complexity spectrum: color patches differing in their saturation, brightness, and hue; and faces differing in weight, age, and gender. Results show typical Garner interference effects for both stimulus sets, although the redundancy gains were rather modest. When a three-dimensional analog of the Garner filtering test is created by allowing a second irrelevant dimension to vary, however, the expected interference effects do not appear. Counter-intuitively, this additional variation often leads to an improvement in performance, an effect which cannot be predicted by the extant models. This effect is shown to be driven primarily by the extra dimension of variation rather than the additional stimuli. The implications for these (and other) findings are considered with regards to the utility of the Garner paradigm and the models that have attempted to describe it.