Much research has been conducted towards the development of fully autonomous unmanned aerial vehicles (UAVs) capable of completing high level mission goals with minimal human interaction. More recently, there is a growing trend to use autonomous systems for smaller-scale missions in urban settings or otherwise tightly constrained environments. For such scenarios, the vehicle must be capable of reliably and accurately performing a variety of complex mission tasks in the absence of a human operator. It follows that robust and efficient obstacle detection and avoidance is a fundamental prerequisite to performing autonomous navigation in an unknown environment. This paper builds upon previous obstacle avoidance work where a pan/tilt-mounted single beam laser rangefinder was validated as an effective means of identifying and characterizing potential obstacles. More specifically, this paper addresses some deficiencies of previously proposed avoidance methodologies by taking a simplified and computationally efficient approach to generating avoidance trajectories. Finally, in order to validate the proposed obstacle detection and avoidance methodology, simulation results and flight test results using the Georgia Tech GTMax UAV helicopter are presented.