We consider the problem of survivable network design in traffic-groomed optical WDM mesh networks that support subwavelength capacity connections. In typical survivable network designs, individual sessions are provided either full protection or no protection. We consider a quality of protection (QoP) framework where a connection is provided partial protection, i.e., when a link failure occurs on the primary path, the protection bandwidth provided on the backup path is less than or equal to the primary bandwidth. Each connection request specifies the primary bandwidth and a minimum backup bandwidth required. The network will guarantee at least the minimum backup bandwidth and, if capacity is available, higher backup bandwidth up to the primary path's bandwidth. The advantage of such a model is that it can reduce backup capacity requirements based on connection needs leading to lower blocking probability and lower network costs. We consider two scenarios: (i) a network with static traffic that is designed using an integer linear program (ILP) formulation and (ii) a network with dynamic traffic for which we present a heuristic connection admission control algorithm that prevents backup resource contention during recovery from a link failure. The results quantify the gain in blocking probability for different partial protection scenarios. The mechanism proposed to counter backup contention is seen to provide an average of 120% reduction in the contention among backup paths of connections traversing a link, especially when the number of wavelengths in each link is small. ©2008 Optical Society of America.