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. Keywords cycle covering, WDM, graph, survivability