The problem of characterizing the relationship between packet size and network delay has received little attention in the field. Research in that area has been limited to either simulation studies or empirical observations that are detached from analytic traffic modeling. From a queueing viewpoint, it is simple to show that these three variables are inter-related, which necessitates are more careful study. We present a traffic model of a router fed by ON/OFF-type sources with heavy-tailed burst sizes. The traffic model considered is consistent with the evidence that Web traffic is heavy-tailed. The analysis cases that are considered establish a quantitative characterization of the complex relationship among packet payload and header sizes, traffic burstiness, and router queuing delay.