This paper investigates proactive packet dropping to achieve transmission energy savings. Such a scheme can be employed for applications which can tolerate a small fraction of packet losses. For a group of packets subject to a single transmission deadline, the optimal dropping scheme (vis-` a-vis total transmission energy) is derived. For packets subject to individual delay constraints, the optimal scheme depends on the energy function and packet sizes. Thus, asymptotically optimal dropping schemes, i. e., when packet size grows large, are pursued. The asymptotically optimal dropping scheme for a single dropped packet is obtained. For dropping more than one packet, two suboptimal, recursive schemes are proposed. These schemes achieve performance very close to the asymptotically optimal schemes as determined by an exhaustive search. Additionally, two performance bounds are derived. It is observed via simulations that significant energy savings are possible via intelligent packet dropping schemes.