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Swarm-based peer-to-peer streaming (SPS) mechanisms tend to generate a significant amount of costly inter-ISP traffic. Localization of overlay connectivity reduces inter-ISP traffic. However, it can adversely affect the delivered quality. In this paper, we systematically examine the performance of SPS for live video over localized overlays. We identify and discuss the fundamental bottlenecks limiting the stream quality and present OLIVES, an ISP-friendly P2P streaming mechanism for live video. OLIVES maintains a fully localized overlay to reduce the volume of inter-ISP traffic and incorporates a two-tier inter-ISP and intra-ISP scheduling scheme to maximize the delivered quality to individual peers. One important design choice is to perform basic scheduling at a substream level and to use implicit coordination among peers. This allows OLIVES to efficiently detect missing blocks and pull them into the ISP in a timely manner with a minimum in coordination overhead. Furthermore, OLIVES incorporates a shortcutting technique that limits the buffer requirements for each participating peer and effectively reduced the playout latency. Through analysis and extensive simulations, we demonstrate the ability of OLIVES to deliver high-quality streams over localized overlays in various realistic scenarios.