Many location-based systems rely on fine-grained tracking of mobile objects that determine their own locations with sensing devices like GPS receivers. For these objects, energy is a very valuable and limited resource. A distance-based reporting protocol can be employed to reduce the energy they consume by sending position updates. However, the energy required for position sensing has not been considered in the past. In this paper, we study how the resulting energy consumption from both sensing and update operations can be reduced for distance-based reporting. We show that significant savings are achieved by sending position updates earlier than actually required. For uniform movement, we derive the minimal power consumption analytically. Subsequently, two novel online heuristics are proposed that control the sending of position updates at runtime. Their effectiveness is validated by extensive simulations.