The development of autonomous lightweight MAVs, capable of navigating in unknown indoor environments, is one of the major challenges in robotics. The complexity of this challenge comes from constraints on weight and power consumption of onboard sensing and processing devices. In this paper we propose the "Droplet" strategy, an avoidance strategy based on stereo vision inputs that outperforms reactive avoidance strategies by allowing constant speed maneuvers while being computationally extremely efficient, and which does not need to store previous images or maps. The strategy deals with nonholonomic motion constraints of most fixed and flapping wing platforms, and with the limited field-of-view of stereo camera systems. It guarantees obstacle-free flight in the absence of sensor and motor noise. We first analyze the strategy in simulation, and then show its robustness in real-world conditions by implementing it on a 20-gram flapping wing MAV.