Advances in technology have led to development of wearable sensing, computing and communication devices that can be woven into the physical environment of our daily lives, enabling a large variety of new applications in several domains including wellness and health care. Despite their tremendous potential to impact our lives, wearable health monitoring systems face a number of hurdles to become a reality. The enabling processors and architectures demand a large amount of energy, requiring sizable batteries. In this chapter, we discuss granular decision making architectures for physical movement monitoring applications. Such modules can be viewed as tiered wake up circuitries. The signal processing based decision making, in combination with a low-power microcontroller, allows for significant power saving through an ultra low-power processing architecture. The significant power saving can be obtained by performing a preliminary ultra low-power signal processing and hence, keeping the microcontroller off when the incoming signal is not of interest. The preliminary signal processing is performed by a set of special purpose functional units, also called screening blocks, that implement template matching functions. Furthermore, an optimization problem is presented, in this chapter, to select screening blocks such that the accuracy requirements of the signal processing are accommodated while the total amount of power is minimized. Finally, this chapter concludes with experimental results on real data from wearable motion sensors. These results show that granular decision making modules fine tuned for signal pre-screening can achieve 63.2% energy saving while maintaining a sensitivity of 94.3% in recognizing physical activities.