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The newly adopted scalable extension of H.264/AVC video coding standard (SVC) demonstrates significant improvements in coding efficiency in addition to an increased degree of supported scalability relative to the scalable profiles of prior video coding standards. Due to the complicated hierarchical prediction structure of the SVC and the concept of key pictures, content-aware rate adaptation of SVC bit streams to intermediate bit rates is a nontrivial task. The concept of quality layers has been introduced in the design of the SVC to allow for fast content-aware prioritized rate adaptation. However, existing quality layer assignment methods are suboptimal and do not consider all network abstraction layer (NAL) units from different layers for the optimization. In this paper, we first propose a technique to accurately and efficiently estimate the quality degradation resulting from discarding an arbitrary number of NAL units from multiple layers of a bitstream by properly taking drift into account. Then, we utilize this distortion estimation technique to assign quality layers to NAL units for a more efficient extraction. Experimental results show that a significant gain can be achieved by the proposed scheme.