Emerging applications such as remote manipulation and remote robotic surgery require communication that is both timely and reliable, but the Internet natively supports only communication that is either completely reliable with no timeliness guarantees (e.g. TCP) or timely with best-effort reliability (e.g. UDP). We present an overlay transport service that can provide highly reliable communication while meeting stringent timeliness guarantees (e.g. 130ms round-trip latency across the US) over the Internet. To enable routing schemes that can support the necessary timeliness and reliability, we introduce dissemination graphs, providing a unified framework for specifying routing schemes ranging from a single path, to multiple disjoint paths, to arbitrary graphs. We conduct an extensive analysis of realworld network data, finding that a routing approach using two disjoint paths performs well in most cases, and that cases where two disjoint paths do not perform well typically involve problems around a source or destination. Based on this analysis, we develop a timely dissemination-graph-based routing method that can add targeted redundancy in problematic areas of the network. This approach can cover over 99% of the performance gap between a traditional single-path approach and an optimal (but prohibitively expensive) scheme, while two dynamic disjoint paths cover about 70% of this gap, and two static disjoint paths cover about 45%. This performance improvement is obtained at a cost increase of about 2% over two disjoint paths.