The serial interval may be defined as the time between the onset of symptoms in an infectious person and the onset of symptoms in a person he or she infects. Several methods of analyzing epidemic data, such as estimates of reproductive numbers, are based on a probability distribution for the serial interval. In this paper, we specify a general SIR epidemic model and prove that the mean serial interval must contract when susceptible persons are at risk of multiple infectious contacts. In an epidemic, the mean serial interval contracts as the prevalence of infection increases. We illustrate two mechanisms through which serial interval contraction can occur: In global competition among infectious contacts, risk of multiple infectious contacts results from a high global prevalence of infection. In local competition among infectious contacts, clustering of contacts places susceptible persons at risk of multiple infectious contacts even when the global prevalence of infection is low. We illustrate these patterns with simulations. We also find that the minimum mean serial interval in a compartmental SIR model becomes arbitrarily small with sufficiently high R_{0}. We conclude that the serial interval distribution is not a stable characteristic of an infectious disease.