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Projecting high-dimensional environment observations into lower-dimensional structured representations can considerably improve data-efficiency for reinforcement learning in domains with limited data such as robotics. Can a single generally useful representation be found? In order to answer this question, it is important to understand how the representation will be used by the agent and what properties such a 'good' representation should have. In this paper we systematically evaluate a number of common learnt and hand-engineered representations in the context of three robotics tasks: lifting, stacking and pushing of 3D blocks. The representations are evaluated in two use-cases: as input to the agent, or as a source of auxiliary tasks. Furthermore, the value of each representation is evaluated in terms of three properties: dimensionality, observability and disentanglement. We can significantly improve performance in both use-cases and demonstrate that some representations can perform commensurate to simulator states as agent inputs. Finally, our results challenge common intuitions by demonstrating that: 1) dimensionality strongly matters for task generation, but is negligible for inputs, 2) observability of task-relevant aspects mostly affects the input representation use-case, and 3) disentanglement leads to better auxiliary tasks, but has only limited benefits for input representations. This work serves as a step towards a more systematic understanding of what makes a 'good' representation for control in robotics, enabling practitioners to make more informed choices for developing new learned or hand-engineered representations.