This paper analyses the design of optimal nonlinear savings taxation, in a multi-period consumption-savings economy where consumers face persistent, uninsurable shocks to the marginal value that they place on consuming. Its main contributions are: (a) to show that shocks of this kind generically justify positive marginal savings taxes, and (b) to characterise these taxes by reference to a limited number of sufficient statistics. The method for obtaining this characterisation is generalisable, and provides a roadmap for reconnecting ‘Mirrleesian’ and ‘sufficient statistics’ approaches to dynamic taxation. Intuitively, dynamic asymmetric information problems imply significant restrictions on intertemporal consumption elasticities. These restrictions keep sufficient statistics representations manageable, despite the multi-dimensional choice setting.