We study the dual problem of image super-resolution (SR), which we term image compact-resolution (CR). Opposite to image SR that hallucinates a visually plausible high-resolution image given a low-resolution input, image CR provides a low-resolution version of a high-resolution image, such that the low-resolution version is both visually pleasing and as informative as possible compared to the high-resolution image. We propose a convolutional neural network (CNN) for image CR, namely, CNN-CR, inspired by the great success of CNN for image SR. Specifically, we translate the requirements of image CR into operable optimization targets for training CNN-CR: the visual quality of the compact resolved image is ensured by constraining its difference from a naively downsampled version and the information loss of image CR is measured by upsampling/super-resolving the compact-resolved image and comparing that to the original image. Accordingly, CNN-CR can be trained either separately or jointly with a CNN for image SR. We explore different training strategies as well as different network structures for CNN-CR. Our experimental results show that the proposed CNN-CR clearly outperforms simple bicubic downsampling and achieves on average 2.25 dB improvement in terms of the reconstruction quality on a large collection of natural images. We further investigate two applications of image CR, i.e., low-bit-rate image compression and image retargeting. Experimental results show that the proposed CNN-CR helps achieve significant bits saving than High Efficiency Video Coding when applied to image compression and produce visually pleasing results when applied to image retargeting.