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 128dimensional 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.