Falls in older people are a major challenge to public health. A wearable fall detector can detect falls automatically based on kinematic information of the human body, allowing help to arrive sooner. To date, most studies have focused on the accuracy of an offline algorithm to distinguish real-world or simulated falls from activities of daily living, while neglecting the false alarm rate and battery life of a real device. To address these two important metrics, which significantly influence user compliance, this paper proposes a low-power fall detector using triaxial accelerometry and barometric pressure sensing. This fall detector minimizes power consumption using both hardware- and firmware-based techniques. Additionally, the fall detection algorithm used in this device is optimized to achieve a balance between sensitivity and false alarm rate, while minimizing the power consumption due to algorithm execution. The fall detector achieved a high sensitivity (91%) with a low false alarm rate (0.1149 alarms per hour), and a commercially-viable battery life (1125 days).