Feeding animals often prefer small, quickly delivered rewards over larger, more delayed rewards. Students of feeding behaviour typically explain this behaviour by saying that animals discount delayed benefits. Temporal discounting implies that delayed benefits are worth less than immediate benefits. This paper presents a new explanation of short–sighted decision–making called the discrimination advantage model that does not rely on discounting. A new model that includes several possible causes of discounting is developed. This model has many interesting features, but it cannot account for two empirical results: the strength of the ‘discounting‘ effect and the fact that the time between choice presentations (the intertrial interval or ITI) has no effect. This leads to the conclusion that although discounting may be important it is probably not a complete explanation of the experimental facts. In the discrimination advantage model the observation that the ITI does not affect choice is seen as a strategy to make a cleaner discrimination between delayed alternatives in a noisy world. A simple example shows that when discrimination is imperfect a short–sighted choice rule can, in some situations, lead to a higher long–term rate than a rule that actually compares long–term rates. This idea is developed and extended in several ways.