In 1-k routing each of the n2 processing units of an n×n mesh connected computer initially holds 1 packet which must be routed such that any processor is the destination of at most k packets. This problem reflects practical desire for routing better than the popular routing of permutations. 1-k routing also has implications for hot-potato worm-hole routing, which is of great importance for real world systems. We present a near-optimal deterministic algorithm running in \sqrt{k} \cdot n / 2 + \go{n} steps. We give a second algorithm with slightly worse routing time but working queue size three. Applying this algorithm considerably reduces the routing time of hot-potato worm-hole routing. Non-trivial extensions are given to the general l-k routing problem and for routing on higher dimensional meshes. Finally we show that k-k routing can be performed in \go{k \cdot n} steps with working queue size four. Hereby the hot-potato worm-hole routing problem can be solved in \go{k^{3/2} \cdot n} steps