Most discriminative techniques for detecting instances from object categories in still images consist of looping over a partition of a pose space with dedicated binary classifiers. The efficiency of this strategy for a complex pose, i.e., for fine-grained descriptions, can be assessed by measuring the effect of sample size and pose resolution on accuracy and computation. Two conclusions emerge: i) fragmenting the training data, which is inevitable in dealing with high in-class variation, severely reduces accuracy; ii) the computational cost at high resolution is prohibitive due to visiting a massive pose partition. To overcome data-fragmentation we propose a novel framework centered on pose-indexed features which assign a response to a pair consisting of an image and a pose, and are designed to be stationary: the probability distribution of the response is always the same if an object is actually present. Such features allow for efficient, one-shot learning of pose-specific classifiers. \\ To avoid expensive scene processing, we arrange these classifiers in a hierarchy based on nested partitions of the pose as in previous work, which allows for efficient search. The hierarchy is then "folded" for training: all the classifiers at each level are derived from one base predictor learned from all the data. The hierarchy is "unfolded" for testing: parsing a scene amounts to examining increasingly finer object descriptions only when there is sufficient evidence for coarser ones. In this way, the detection results are equivalent to an exhaustive search at high resolution. We illustrate these ideas by detecting and localizing cats in highly cluttered greyscale scenes.