In low-power sensing systems, communication constraints play a critical role; e.g., biomedical devices often acquire physiological signals from distributed sources and/or wireless implants. Compressive sensing enables sub-Nyquist sampling for low-energy data reduction on such nodes. The reconstruction cost, however, is severe, typically pushing signal analysis to a base station. We present a seizure-detection processor that directly analyzes compressively-sensed electroencephalograms (EEGs) on the sensor node. In addition to alleviating communication costs while also circumventing reconstruction costs, it leads to computational energy savings, due to the reduced number of input samples. This provides an effective knob for system power management and enables scaling of energy and application-level performance. For compression factors of 2-24x, the energy to extract signal features (over 18 channels) is 7.13-0.11/iJ, and the detector's performance for sensitivity, latency, and specificity is 96-80%, 4.7-17.8 sec, and 0.15-0.79 false-alarms/hr., respectively (compared to baseline performance of 96%, 4.6 sec, and 0.15 false-alarms/hr.).