We accelerate volumetric obscurance, a variant of ambient occlusion, and solve undersampling artifacts, such as banding, noise or blurring, that screen-space techniques traditionally suffer from. We make use of an efficient statistical model to evaluate the occlusion factor in screen-space using a single sample. Overestimations and halos are reduced by an adaptive layering of the visible geometry. Bias at tilted surfaces is avoided by projecting and evaluating the volumetric obscurance in tangent space of each surface point. We compare our approach to several traditional screen-space volumetric obscurance techniques and show its competitive qualitative and quantitative performance. Our algorithm maps well to graphics hardware, does not require the traditional bilateral blur step of previous approaches, and avoids typical screen-space related artifacts such as temporal instability due to undersampling.