The increasing popularity of head-mounted devices and 360-degree video cameras allows content providers to provide virtual reality (VR) video streaming over the Internet, using a two-dimensional representation of the immersive content combined with traditional HTTP adaptive streaming (HAS) techniques. However, since only a limited part of the video (i.e., the viewport) is watched by the user, the available bandwidth is not optimally used. Recent studies have shown the benefits of adaptive tile-based video streaming; rather than sending the whole 360-degree video at once, the video is cut into temporal segments and spatial tiles, each of which can be requested at a different quality level. This allows prioritization of viewable video content, and thus results in increased bandwidth utilization. Given the early stages of research, there are still a number of open challenges to unlock the full potential of adaptive tile-based VR streaming. The aim of this work is to provide an answer to several of these open research questions. Among others, we propose two tile-based rate adaptation heuristics for equirectangular VR video, which use the great-circle distance between the viewport center and the center of each of the tiles to decide upon the most appropriate quality representation. We also introduce a feedback loop in the quality decision process, which allows the client to revise prior decisions based on more recent information on the viewport location. Furthermore, we investigate the benefits of parallel TCP connections and the use of HTTP/2 as an application layer optimization. Through an extensive evaluation, we show that the proposed optimizations result in a significant improvement in terms of video quality (more than twice the time spent on the highest quality layer), compared to non-tiled HAS solutions.