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Off-chip substrate routing for high-density packages is on the critical path for time to market. Compared with on-chip routers, existing commercial tools for off-chip routing have lower routability and often result in a large number of unrouted nets for manual routing. In this paper, we explain why planar routing is still required with multiple routing layers for substrate routing and then propose a flexible via-staggering technique to improve routability. In addition, we develop an efficient yet effective substrate routing algorithm, applying dynamic pushing to tackle the net ordering problem and reordering and rerouting to further reduce wire length and congestion. Compared with an industrial design tool that leaves 936 nets unrouted for nine industrial designs with a total of 6100 nets, our algorithm reduces the unrouted nets to 212, a 4.5-times net number reduction, which translates to design time reduction.