Network survivability is a critical issue for modern fiber-optic telecommunication networks. Networks with alternate routes between pairs of nodes permit users to communicate in the face of equipment failure. In this paper, we consider the following low-connectivity network design (LCND) problem. Given a graph G=(N,E) and a connectivity requirement o(i) in (0,1,2) for each node, design a network at minimum cost that contains at least o(st) = min(o(s),o(t)) disjoint paths between nodes s and t. We present linear time algorithms for both node- and edge-connectivity versions of the problem on series-parallel graphs. Due to the sparsity of telecommunications networks this algorithm can be applied to obtain partial solutions and decompositions, that may be embedded in a heuristic solution procedure as well as exact solution algorithms for the problem on general graphs.