According to the antagonistic pleiotropy theory of ageing, natural selection has favoured genes conferring short-term benefits to the organism at the cost of deterioration in later life. The 'disposable soma' theory expresses this as a life-history strategy in which somatic maintenance is below the level required to prevent ageing, thus enabling higher immediate fertility. It has been argued that a non-ageing strategy will always be bettered by a low but non-zero rate of ageing, because the costs of such ageing will be felt only in the distant future when they are of negligible importance. Here, we examine this argument critically. We find that a non-ageing strategy will be locally optimal if, in the presence of ageing, the onset of deterioration is sufficiently rapid or early. Conversely, ageing will be optimal if deterioration is sufficiently slow or late. As the temporal profile of ageing changes from one of steady deterioration to one involving a sudden loss of vitality after a period of little or no decline, the conditions for a non-ageing strategy to be locally optimal become progressively more stringent. But for all forms of profile considered, conditions can be found for which a strategy involving no ageing is locally optimal.