A common approach for establishing connection requests in an optical ring network that uses wavelength-division multiplexing is to first find a routing of the requests that minimizes the congestion and then deal with the wavelength allocation. The congestion of a routing, however, does not reflect its wavelength requirements. Indeed, we observe that for certain instances such an approach can result in considerable waste of network resources. To overcome this, we propose a new routing objective, namely to minimize the maximum clique of the routing, i.e., the maximum number of connections that pairwise share a common fiber. We present optimal algorithms and heuristics for finding minimum clique routings and perform experiments to evaluate their performance.