We review approaches to formulating and solving for optimal tax problems in heterogeneous-agent economies. We show that whether worker heterogeneity is represented through a small or a large number of different types is not just a technical detail but has an important impact on practical Mirrleesian policy prescriptions. In particular, the coarseness of the grid for productivity appears as a novel element in the Diamond-Saez implicit optimal tax formula, and numerical simulations suggest that the optimal policy varies considerably with this coarseness. We also show that popular computational approaches that solve jointly for allocations and taxes fail to recover the constrained efficient allocation unless a very fine productivity grid is used. We conclude that Mirrleesian policy prescriptions based on a coarse grid should not be taken seriously. If using a very fine grid is impractical, then optimizing within a flexible parametric class is preferable to the non-parametric Mirrleesian approach.