The binary descriptors are the representation of choice for real-time keypoint matching. However, they suffer from reduced matching rates due to their discrete nature. We propose an approach that can augment their performance by searching in the top K near neighbor matches instead of just the single nearest neighbor one. To pick the correct match out of the K near neighbors, we exploit statistics of descriptor variations collected for each keypoint in an off-line training phase. This is a similar approach to those that learn a patch specific keypoint representation. Unlike these approaches, we only use a keypoint specific score to rank the list of K near neighbors. Since this list can be efficiently computed with approximate nearest neighbor algorithms, our approach scales well to large descriptor sets.