Inverse Reinforcement Learning (IRL) allows a robot to generalize from demonstrations to previously unseen scenarios by learning the demonstrator’s reward function. However, in multi-step tasks, the learned rewards might be delayed and hard to directly optimize. We present Sequential Windowed Inverse Reinforcement Learning (SWIRL), a three-phase algorithm that partitions a complex task into shorter-horizon subtasks based on Switched Linear Dynamical transitions that occur consistently across demonstrations. SWIRL then learns a sequence of local reward functions that describe the motion between transitions. Once these reward functions are learned, SWIRL applies Q-learning to compute a policy that maximizes the rewards. We compare SWIRL (demonstrations to segments to rewards) with Supervised Policy Learning (SPL - demonstrations to policies) and Maximum Entropy IRL (MaxEnt-IRL demonstrations to rewards) on standard Reinforcement Learning benchmarks: Parallel Parking with noisy dynamics, Two-Link acrobot, and a 2D GridWorld. We find that SWIRL converges to a policy with similar success rates (60%) in 3x fewer time-steps than MaxEnt-IRL, and requires 5x fewer demonstrations than SPL. In physical experiments using the da Vinci surgical robot, we evaluate the extent to which SWIRL generalizes from linear cutting demonstrations to cutting sequences of curved paths.