Back- and front-vertex powers are concepts of some importance in clinical practice. For example, the former is used for characterizing the typical spectacle lens and the latter for characterizing the addition of a bifocal lens. Typically, they are defined either in terms of vergence or the distance to a focal point. This note argues that current definitions are not as clear as they might be, that there is an unnecessary asymmetry between the definitions of front- and back-vertex powers, and that they are designed primarily for systems that are not astigmatic. The purpose of this note is to offer modified definitions that hold for optical systems in general, that is, for systems that may contain astigmatic and decentered refracting elements. The definitions are conceptually clear and provide a simpler derivation of Keating's elegant and general expressions for back- and front-vertex powers.