This paper presents a routing strategy called Pivot Interval Routing (PIR), which allows message routing on every weighted n-node network along paths whose stretch (namely, the ratio between their length and the distance between their endpoints) is at most five, and whose average stretch is at most three, with routing tables of size O( p n log 3=2 n) bits per node. In addition, the route lengths are at most 2D (d1:5De for uniform weights) where D is the weighted diameter of the network. Moreover, it is shown that the PIR strategy can be constructed in polynomial time and can be implemented so that the generated scheme is in the form of an interval routing scheme (IRS), using at most O( p n log n) intervals per link. As a result, the schemes are simpler than previous ones and they imply that the paths followed by messages are loop-free. On the other hand, we show that there is no loop-free routing strategy guaranteeing a memory bound of at most p n bits per node for a..