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We investigate three schemes for severe compression of iris images in order to assess what their impact would be on recognition performance of the algorithms deployed today for identifying people by this biometric feature. Currently, standard iris images are 600 times larger than the IrisCode templates computed from them for database storage and search; but it is administratively desired that iris data should be stored, transmitted, and embedded in media in the form of images rather than as templates computed with proprietary algorithms. To reconcile that goal with its implications for bandwidth and storage, we present schemes that combine region-of-interest isolation with JPEG and JPEG2000 compression at severe levels, and we test them using a publicly available database of iris images. We show that it is possible to compress iris images to as little as 2000 bytes with minimal impact on recognition performance. Only some 2% to 3% of the bits in the IrisCode templates are changed by such severe image compression, and we calculate the entropy per code bit introduced by each compression scheme. Error tradeoff curve metrics document very good recognition performance despite this reduction in data size by a net factor of 150, approaching a convergence of image data size and template size.