The point-to-point connection problem is to find a subset of arcs with minimal total cost connecting a fixed number of source-destination pairs. The problem has many variations for different applications. In this paper, we focus on a case where the source-destination pairs are prematched. We examine the structure of the problem with two source-destination pairs and provide an efficient implementation of a Dijkstra-like algorithm with time complexity O(mn + n(2) log n). We also provide a dynamic programming algorithm with complexity O(n(11)) for the case with three source-destination pairs. We conjecture that the same approach can be generalized for p source-destination pairs with complexity O(n(3p+2)) where p is fixed.