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It is well known that when the two eyes are provided with two views of different resolutions the overall perception is dominated by the high resolution view. This property, known as binocular suppression, is effectively used to reduce the bit rate required for stereoscopic video delivery, where one view of the stereo pair is encoded at a much lower quality than the other. There have been significant amount of effort in the recent past to measure the just noticeable level of asymmetry between the two views, where asymmetry is achieved by encoding views at two quantization levels. However, encoding artifacts introduce both blurring and blocking artifacts in to the stereo views, which are perceived differently by the human visual system. Therefore, in this paper, we design a set of psycho-physical experiments to measure the just noticeable level of asymmetric blur at various spatial frequencies, luminance contrasts and orientations. The subjective results suggest that humans could tolerate a significant amount of asymmetry introduced by blur, and the level of tolerance is independent of the spatial frequency or luminance contrast. Furthermore, the results of this paper illustrate that when asymmetry is introduced by unequal quantization, the just noticeable level of asymmetry is driven by the blocking artifacts. In general, stereoscopic asymmetry introduced by way of asymmetric blurring is preferred over asymmetric compression. It is expected that the subjective results of this paper will have important use cases in objective measurement of stereoscopic video quality and asymmetric compression and processing of stereoscopic video.