Primates can easily identify visual objects over large changes in retinal position--a property commonly referred to as position "invariance." This ability is widely assumed to depend on neurons in inferior temporal cortex (IT) that can respond selectively to isolated visual objects over similarly large ranges of retinal position. However, in the real world, objects rarely appear in isolation, and the interplay between position invariance and the representation of multiple objects (i.e., clutter) remains unresolved. At the heart of this issue is the intuition that the representations of nearby objects can interfere with one another and that the large receptive fields needed for position invariance can exacerbate this problem by increasing the range over which interference acts. Indeed, most IT neurons' responses are strongly affected by the presence of clutter. While external mechanisms (such as attention) are often invoked as a way out of the problem, we show (using recorded neuronal data and simulations) that the intrinsic properties of IT population responses, by themselves, can support object recognition in the face of limited clutter. Furthermore, we carried out extensive simulations of hypothetical neuronal populations to identify the essential individual-neuron ingredients of a good population representation. These simulations show that the crucial neuronal property to support recognition in clutter is not preservation of response magnitude, but preservation of each neuron's rank-order object preference under identity-preserving image transformations (e.g., clutter). Because IT neuronal responses often exhibit that response property, while neurons in earlier visual areas (e.g., V1) do not, we suggest that preserving the rank-order object preference regardless of clutter, rather than the response magnitude, more precisely describes the goal of individual neurons at the top of the ventral visual stream.