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The volume of Internet video is growing, and is expected to exceed 57 percent of global consumer Internet traffic by 2014. Peer-to-Peer technology can help delivering this massive volume of traffic in a cost-efficient, scalable, and reliable manner. However, single bit rate streaming is not sufficient given today's device and network connection diversity. A possible solution to this problem is provided by layered coding techniques, such as Scalable Video Coding, which allow addressing this diversity by providing content in various qualities within a single bit stream. In this paper we propose a new self-adapting piece-picking algorithm for downloading layered video streams, called Deftpack. Our algorithm significantly reduces the number of stalls, minimises the frequency of quality changes during playback, and maximizes the effective usage of the available bandwidth. Deftpack is the first algorithm that is specifically crafted to take all these three quality dimensions into account simultaneously, thus increasing the overall quality of experience. Additionally, Deftpack can be integrated into Bit torrent-based P2P systems and so has the chance of large-scale deployment. Our results from realistic swarm simulations show that Deftpack significantly outperforms previously proposed algorithms for retrieving layered content when all three quality dimensions are taken into account.