Video streaming is predicted to become the dominating traffic in mobile broadband networks. At the same time, adaptive HTTP streaming is developing into the preferred way of streaming media over the Internet. In this paper, we evaluate how different components of a streaming system can be optimized when serving content to mobile devices in particular. We first analyze the media traffic from a Norwegian network and media provider. Based on our findings, we outline benefits and challenges for HTTP streaming, on the sender and the receiver side, and we investigate how HTTP-based streaming affects server performance. Furthermore, we discuss various aspects of efficient coding of the video segments from both performance and user perception point of view. The final part of the paper studies efficient adaptation and delivery to mobile devices over wireless networks. We experimentally evaluate and improve adaptation strategies, multilink solutions, and bandwidth prediction techniques. Based on the results from our evaluations, we make recommendations for how an adaptive streaming system should handle mobile devices. Small changes, or simple awareness of how users perceive quality, can often have large effects.