Peer-assisted delivery of video content has shown a great potential to reduce upload bandwidth requirements for content providers by exploiting idle client resources in the video dissemination process. As primary content sources, the servers run by content providers play a critical role in such systems, making their adequate provisioning a key part of the streaming mechanism. While dynamic resource provisioning has been studied before, little is known about resource allocation for streaming of scalable media content. Besides the pure amount of resources, here, the quality level of the delivered video content becomes relevant. The spreading of video blocks with the wrong quality can lead to situations where peers are forced to reduce their video qualities, despite them having enough download capacity. To address this problem, in this paper, a new SVC-based adaptation policy and a request-based extension to it are proposed, enabling content providers to manage their streaming services in a video quality-aware manner. Prototypical evaluations show that the mechanisms outperform existing quality-agnostic approaches in terms of delivered SVC video quality.