A promising alternative for treating absence seizures has emerged through closed-loop neurostimulation, which utilizes a wearable or implantable device to detect and subsequently suppress epileptic seizures. Such devices should detect seizures fast and with high accuracy, while respecting the strict energy budget on which they operate. Previous work has overlooked one or more of these requirements, resulting in solutions which are not suitable for continuous closed-loop stimulation. In this paper, we perform an in-depth design space exploration of a novel seizure-detection algorithm, which uses a complex Morlet wavelet filter and a static thresholding mechanism to detect absence seizures. We consider both the accuracy and speed of our detection algorithm, as well as various trade-offs with device autonomy when executed on a low-power processor. For example, we demonstrate that a minimal decrease in average detection rate of only 1.83% (from 92.72% to 90.89%) allows for a substantial increase in device autonomy (of 3.7x) while also facilitating faster detection (from 710 ms to 540 ms).