In packetized media streaming systems, packet dependencies are often modeled as a directed acyclic graph called the dependency graph. We consider the situation where the dependency graph is reducible to a tree. This occurs, for instance, in MPEG1 video streams that are packetized at the frame level. Other video coding standards such as H.264 also allow tree-reducible dependencies. We propose in this context efficient dynamic programming algorithms for finding rate-distortion optimal transmission policies. The proposed algorithms are much faster than previous exact algorithms developed for arbitrary dependency graphs.