We present Model Predictive Planning (MPP), a trajectory planner for low-agility vehicles such as a fixed-wing aircraft to navigate obstacle-laden environments. MPP consists of (1) a multi-path planning procedure that identifies candidate paths, (2) a raytracing procedure that generates linear constraints around these paths to enforce obstacle avoidance, and (3) a convex quadratic program that finds a feasible trajectory within these constraints if one exists. Low-agility aircraft cannot track arbitrary paths, so refining a given path into a trajectory that respects the vehicle's limited maneuverability and avoids obstacles often leads to an infeasible optimization problem. The critical feature of MPP is that it efficiently considers multiple candidate paths during the refinement process, thereby greatly increasing the chance of finding a feasible and trackable trajectory. We demonstrate the effectiveness of MPP on a longitudinal aircraft model.