In this paper, we present a novel method to improve the flexibility of descriptor matching for image recognition by using local multiresolution pyramids in feature space. We propose that image patches be represented at multiple levels of descriptor detail and that these levels be defined in terms of local spatial pooling resolution. Preserving multiple levels of detail in local descriptors is a way of hedging one's bets on which levels will most relevant for matching during learning and recognition. We introduce the Pyramid SIFT (P-SIFT) descriptor and show that its use in four state-of-the-art image recognition pipelines improves accuracy and yields state-of-the-art results. Our technique is applicable independently of spatial pyramid matching and we show that spatial pyramids can be combined with local pyramids to obtain further improvement. We achieve state-of-the-art results on Caltech-101 (80.1%) and Caltech-256 (52.6%) when compared to other approaches based on SIFT features over intensity images. Our technique is efficient and is extremely easy to integrate into image recognition pipelines.