Compensatory or catch-up growth (CG) is widely observed following periods of resource deprivation. Because of this commonness, it is generally assumed that compensatory growth is adaptive, but most theory to date has explicitly ignored considerations of fitness. Following a period of deprivation, when resources become plentiful again, individuals may not respond at all and continue on a "normal" trajectory from a smaller size at age, may exhibit faster-than-normal growth immediately following the end of the period, or may adopt a growth strategy that involves faster-than-normal growth at some later time. Compensating individuals may also overtake control individuals who have been growing normally throughout. We hypothesize that the key to understanding CG is that growth leads to the accumulation of damage at the cellular level that is expressed (and thus must be modeled) at the level of the organism. We show that a life-history model incorporating the mortality consequences of both size and damage provides a framework for understanding compensatory growth. We use the theory to classify physiological and life-history characteristics for which CG is predicted to be the optimal response to deprivation.