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An orientation of an undirected graph is a choice of direction for each of its edges. An orientation is called ideal with respect to a given set of pairs of vertices if it does not increase the shortest-path distances between the members of any of the pairs. A polynomial-time algorithm is given for constructing an ideal orientation with respect to two given pairs and any positive edge-lengths, or else recognizing that no such orientation exists. Moreover, we show that this problem is in thedoi:10.1016/0024-3795(89)90481-3 fatcat:w5f54xcluret5e3tekxskfmv4i