In a technique called depth image based rendering, new images are generated using information from an original source image and its corresponding depth map, such that the new images appear to have been taken from different camera viewpoints. This technique is bandwidth-efficient and is ideal for multiview display systems, such as autostereoscopic 3D-TV. In a previous study, we demonstrated that uniform smoothing of depth maps through Gaussian filtering helps improve the image quality of the rendered images. In the present study we investigated the potential benefits of two non-uniform smoothing methods: asymmetric smoothing, where the horizontal extent of smoothing was smaller than that in the vertical direction, and adaptive smoothing, where the level and extent of smoothing was based on the local depth magnitude. In this vein, ten viewers assessed image quality and depth quality of four stereoscopic images in which the view to one eye was a rendered image based on one of the three smoothing methods: uniform, asymmetric, or adaptive. The experimental results showed an improvement in ratings of image quality for all three methods as the level of smoothing was increased. The results also indicated a slight advantage in image quality for asymmetric smoothing over the other two methods. Ratings of overall depth quality were significantly higher than corresponding non-stereoscopic references for all three methods, although the ratings decreased at the highest level of smoothing that was used in the present study. In general, ratings of depth quality tended to be marginally lower for the asymmetric method.