Detecting small obstacles on the road ahead is a critical part of the driving task which has to be mastered by fully autonomous cars. In this paper, we present a method based on stereo vision to reliably detect such obstacles from a moving vehicle. The proposed algorithm performs statistical hypothesis tests in disparity space directly on stereo image data, assessing freespace and obstacle hypotheses on independent local patches. This detection approach does not depend on a global road model and handles both static and moving obstacles. For evaluation, we employ a novel lost-cargo image sequence dataset comprising more than two thousand frames with pixelwise annotations of obstacle and free-space and provide a thorough comparison to several stereo-based baseline methods. The dataset will be made available to the community to foster further research on this important topic. The proposed approach outperforms all considered baselines in our evaluations on both pixel and object level and runs at frame rates of up to 20 Hz on 2 mega-pixel stereo imagery. Small obstacles down to the height of 5 cm can successfully be detected at 20 m distance at low false positive rates.