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Removal of rain streaks from a single image is an extremely challenging problem since the rainy images often contain rain streaks of different size, shape, direction and density. Most recent methods for deraining use a deep network following a generic "encoder-decoder" architecture which captures low-level features across the initial layers and high-level features in the deeper layers. For the task of deraining, the rain streaks which are to be removed are relatively small and focusing much on global features is not an efficient way to solve the problem. To this end, we propose using an overcomplete convolutional network architecture which gives special attention in learning local structures by restraining the receptive field of filters. We combine it with U-Net so that it does not lose out on the global structures as well while focusing more on low-level features, to compute the derained image. The proposed network called, Over-and-Under Complete Deraining Network (OUCD), consists of two branches: overcomplete branch which is confined to small receptive field size in order to focus on the local structures and an undercomplete branch that has larger receptive fields to primarily focus on global structures. Extensive experiments on synthetic and real datasets demonstrate that the proposed method achieves significant improvements over the recent state-of-the-art methods.