In battery-operated wireless video surveillance systems (WVSS), it is mostly required to detect events in an energy-efficient manner due to limited available energy and a huge amount of data to be processed. Therefore, one of the main challenges in the battery-constrained systems is to minimize the energy consumption of the whole system. In this paper, we present an energy-aware event detector which has a hierarchical decision architecture to maximize the system lifetime while achieving the required detection accuracy. An analytical model for the relationship between the complexity of the event detector and system performance is derived based on the given event characteristics. Finally, we suggest a heuristic search algorithm to significantly reduce the heavy computational complexity. Experimental results have shown that the proposed heuristic search algorithm provides 98.17% complexity reduction on average with a negligible deterioration of the system lifetime.