This paper focuses on energy-efficient packet transmission with individual packet delay constraints. The optimal offline scheduler (vis-a-vis total transmission energy), assuming information of all packet arrivals before scheduling, was developed by Zafer, et al. (2005) and Chen et al. (2006). This paper shows that when packet inter-arrival times are identically and independently distributed (Ltd.), the resulting optimal transmission durations of packets m and M - m +1, m epsiv [1, .. ., M], M ges 1, are identically distributed. This symmetry property leads to a simple and exact solution of the average packet delay under the optimal offline schedule. Two heuristic online scheduling algorithms, which assume no future arrival information, are then studied. These online schedulers are compared with the optimal offline scheduler in terms of delay and energy performance via analysis and simulations. While both online schedulers are inherently inferior, one online scheduler is shown to achieve a comparable energy performance to the optimal offline scheduler in a wide range of scenarios.