Connection availability is considered as a critical metric when providing differentiated services in Wavelength-Division Multiplexing mesh networks. Indeed, one of the major concerns of optical network operators is related to improving the availability of services provided to their highest-class clients. Achieving this objective is possible through managing faults using the different classical protection schemes, namely the so-called dedicated and shared protection schemes. However, the majority of the work concerning protection schemes has considered the primary connections as equally important when contending for the use of the backup resources. As a main contribution in this paper, we therefore propose an improvement of the existing protection schemes through the introduction of relative priorities among the different primary connections contending for the access to the protection path. To evaluate numerically the benefits of the service differentiation feature introduced in our proposal, we first develop a mathematical model, based on which we derive explicit expressions for the average connection availabilities that result from both the classical protection schemes and the proposed priority-aware one. Through this model, we show how the availability of the highest-class clients is improved when deploying the proposed priority-aware protection scheme. Finally, with the same objective in mind, we develop a simulation study, where a given set of connection demands with predefined availability requirements is provisioned using different protection strategies. Through this study, we show that the priority-aware protection strategy satisfies service-availability requirements in a cost-effective manner compared with the classical protection schemes.