The efficient coding hypothesis posits that sensory systems are adapted to the statistics of their inputs, maximizing mutual information between environmental signals and their representations, subject to biological constraints. While elegant, information theoretic quantities are notoriously difficult to measure or optimize, and most research on the hypothesis employs approximations, bounds, or substitutes (e.g., reconstruction error). A recently developed measure of coding efficiency, the "manifold capacity", quantifies the number of object categories that may be represented in a linearly separable fashion, but its calculation relies on a computationally intensive iterative procedure that precludes its use as an objective. Here, we simplify this measure to a form that facilitates direct optimization, use it to learn Maximum Manifold Capacity Representations (MMCRs), and demonstrate that these are competitive with state-of-the-art results on current self-supervised learning (SSL) recognition benchmarks. Empirical analyses reveal important differences between MMCRs and the representations learned by other SSL frameworks, and suggest a mechanism by which manifold compression gives rise to class separability. Finally, we evaluate a set of SSL methods on a suite of neural predictivity benchmarks, and find MMCRs are highly competitive as models of the primate ventral stream.