Not all people are equally easy to identify: color statistics might be enough for some cases while others might require careful reasoning about high-and low-level details. However, prevailing person re-identification (re-ID) methods use one-size-fits-all high-level embeddings from deep convolutional networks for all cases. This might limit their accuracy on difficult examples or makes them needlessly expensive for the easy ones. To remedy this, we present a new person re-ID model that combines effective embeddings built on multiple convolutional network layers, trained with deep-supervision. On traditional re-ID benchmarks, our method improves substantially over the previous state-of-the-art results on all five datasets that we evaluate on. We then propose two new formulations of the person re-ID problem under resource-constraints, and show how our model can be used to effectively trade off accuracy and computation in the presence of resource constraints.