Screen-space ambient occlusion (SSAO) shows high efficiency and is widely used in real-time 3D applications. However, using SSAO algorithms in stereo rendering can lead to inconsistencies due to the differences in the screen-space information captured by the left and right eye. This will affect the perception of the scene and may be a source of viewer discomfort. In this paper, we show that the raw obscurance estimation part and subsequent filtering are both sources of inconsistencies. We developed a screen-space method involving both views in conjunction, leading to a stereo-aware raw obscurance estimation method and a stereo-aware bilateral filter. The results show that our method reduces stereo inconsistencies to a level comparable to geometry-based AO solutions, while maintaining the performance benefits of a screen-space approach.