Constraints on supernova-driven galactic winds from elliptical galaxies at the epoch of star formation are investigated. The occurrence of mass loss is found to depend critically on the supernova rate in the case of dwarf galaxies, while the depth of the potential well is the most important constraint for giant ellipticals. The smallest dwarf ellipticals must have evolved from significantly more massive progenitors in order to have sustained a wind that carried away most of their metal production.