High functional complexity is leading us towards new architectures for sensing systems. Multi-tiered design is one among the many emerging alternatives. Such architectures bring new opportunities for effective system-level power management. For instance, varying one/more tier-level parameters can provide substantial end-to-end energy scaling. In this paper, we review an existing approach that shows how one such parameter, namely data compression, can help us scale energy at the cost of algorithmic accuracy. The methodology is driven by a case study of inferring the onset of seizure events directly from compressively-sensed electroencephalograms. Results from an integrated circuit implementation have shown tier-level computational energy scaling in the range 1.2-214 μJ depending on the amount of compression (2-24×) and inference accuracy (sensitivity, latency, and specificity of 91-96%, 4.7-5.3 sec., and 0.17-0.30 false-alarms/hr., respectively). The projections we make in this paper show that for similar systems, compressive sensing, through this approach, has the potential to prolong battery lives of all tiers by up to 5×.