The iterated Prisoner's Dilemma re#ects the essence of repeated cooperative interactions with sel"sh incentives. However, the classical form of this game assumes that individuals either cooperate or defect, whereas in practice di!erent degrees of cooperation are usually possible. To overcome this limitation, we present a model of alternating cooperative trade in which individuals controlled the costs they incurred in bene"ting their partners. Since the range of possible strategies is enormous, competitively successful solutions were identi"ed using a genetic algorithm, a powerful search technique in which good performers are iteratively selected and recombined from an initial &&strategy soup''. Beginning with a population of asocial individuals, altruistic behaviour readily emerged. Like the pre-de"ned strategy of &&Raise-the-Stakes'', the emerging strategies evolved protection from cheats by investing relatively little in strangers and subsequently responding quantitatively to a partner's altruism. Unlike &&Raisethe-Stakes'', they began trading relations at intermediate levels and, when the bene"t-to-cost ratio of cooperation was relatively low, mean investment was considerably below the maximum level. Our approach is novel in allowing us to predict not just whether cooperation will occur, but how cooperative individuals will be, in relation to factors such as the number of rounds and the cost e!ectiveness of cooperative trade.