We present images with binary codes in a way that balances discrimination and learnability of the codes. In our method, each image claims its own code in a way that maintains discrimination while being predictable from visual data. Category memberships are usually good proxies for visual similarity but should not be enforced as a hard constraint. Our method learns codes that maximize separability of categories unless there is strong visual evidence against it. Simple linear SVMs can achieve state-of-the-art results with our short codes. In fact, our method produces state-of-the-art results on Caltech256 with only 128-dimensional bit vectors and outperforms state of the art by using longer codes. We also evaluate our method on ImageNet and show that our method outperforms state-of-the-art binary code methods on this large scale dataset. Lastly, our codes can discover a discriminative set of attributes.