Wearables are being widely utilized in health and wellness applications, primarily due to the recent advances in sensor and wireless communication, which enhance the promise of wearable systems in providing continuous and real-time monitoring and interventions. Wearables are generally composed of hardware/software components for collection, processing, and communication of physiological data. Practical implementation of wearable monitoring in real-life applications is currently limited due to notable obstacles. The wearability and form factor are dominated by the amount of energy needed for sensing, processing, and communication. In this article, we propose an ultra-low-power granular decision-making architecture, also called screening classifier, which can be viewed as a tiered wake-up circuitry, consuming three orders of magnitude-less power than the state-of-the-art low-power microcontrollers. This processing model operates based on computationally simple template matching modules, based on coarse- to fine-grained analysis of the signals with on-demand and gradually increasing the processing power consumption. Initial template matching rejects signals that are clearly not of interest from the signal processing chain, keeping the rest of processing blocks idle. If the signal is likely of interest, the sensitivity and the power of the template matching modules are gradually increased, and ultimately, the main processing unit is activated. We pose optimization techniques to efficiently split a full template into smaller bins, called mini-templates, and activate only a subset of bins during each classification decision. Our experimental results on real data show that this signal screening model reduces power consumption of the processing architecture by a factor of 70% while the sensitivity of detection remains at least 80%.