This paper considers the design of a survivable WDM network based on covering the initial network with sub-networks, which are protected independently from each other. We focus on the case where the optical WDM network is a ring, there are requests between any pair of vertices and the covering is done with small cycles. This problem can be modelled as follows: Find a covering of the edges of a logical graph I (here the complete graph Kn ) by subgraphs Ik of a certain kind (here cycles Ck of length k), such that, for each Ik , there exists in the physical graph G (here Cn ) a disjoint routing of the edges of Ik . The aim is to minimize the number of subgraphs Ik in the covering. We give optimal solutions for that problem.