The design of a survivable network with pathprotection involves the provisioning of a primary and a backup path for every connection request. To optimize bandwidth usage under path-based protection, backup paths are allowed to share bandwidth under single failure model. However, path-based protection does not guarantee fast recovery as switches along a shared backup path may need to be reconfigured according to the particular primary path that needs to be recovered. Pre-crossconnected trail (PXT) addresses this problem by ensuring that backup paths are pre-connected. In practice, different requests may have different tolerance for recovery time. However, PXT does not consider differentiated tolerance and thus may block connections that may tolerate longer recovery times. In this paper, we address the problem of provisioning WDM networks with differentiated quality of protection under the path-based protection scheme. We formulate the problem of path protection with Differentiated Quality-of-Protection (DQoP) under single failure model, and develop an on-line algorithm that relaxes the PXT scheme by enabling the provisioning of requests under two classes of protection services. We consider both node failures as well as link failures. Extensive simulation results on several network topologies and under different traffic models confirm a reduction of up to 13% in blocking probability and up to 4% in bandwidth usage compared to the conventional PXT scheme.