Almost everyone believes that freedom from deprivation should have significant weight in specifying what justice between generations requires. Some theorists hold that it should always trump other distributive concerns. Other theorists hold that it should have some but not lexical priority. I argue instead that freedom from deprivation should have lexical priority in some cases, yet weighted priority in others. More specifically, I defend semi-strong sufficientarianism. This view posits a deprivation threshold at which people are free from deprivation, and an (...) affluence threshold at which people can live an affluent life, even though their lives may be even further improved beyond that point. I argue that freedom from deprivation in one generation lexically outweighs providing affluence in another generation; in all other cases, freedom from deprivation does not have lexical priority. (shrink)