In Experiment 1, pigeons responded on concurrent-chains schedules with equal variable-interval schedules as initial links and fixed delays to food as terminal links. One terminal-link delay was always three times as long as the other. As terminal-link delays increased, response percentages on the key with the shorter terminal link increased according to a curvilinear function. This result supported the predictions of the hyperbolic value-added model and the contextual-choice theory but not delay-reduction theory. In Experiment 2, the terminal links were always delays of 2s and 12s, followed by food, and the durations of the initial links varied across conditions. As initial-link durations increased, pigeons' response percentages on the key with the shorter terminal link decreased, but toward an asymptote greater than 50%, indicating a continued preference for the shorter terminal link with very long initial links. This result was more consistent with the predictions of the hyperbolic-value added model than with those of the contextual-choice model or of delay-reduction theory.