We present a grid-based 3D reconstruction method which integrates all costs given by stereo vision into what we call a Cost-Curve Occupancy Grid (CCOG). Occupancy probabilities of grid cells are estimated in a Bayesian formulation, from the likelihood of stereo cost measurements taken at all distance hypotheses. This is accomplished with only a small set of probabilistic assumptions which we discuss in the paper. We quantitatively characterize the method's performance under different conditions of both image noise and number of used stereo pairs, compared also to traditional algorithms. We complement the study by giving insights on design choices of CCOGs such as likelihood model, window size of the cost function and use of a hole filling method. Experiments were made on a real-world outdoors dataset with ground-truth data.