Wavelength division multiplexing (WDM) networks are matured to provide, scalable data centric infrastructure, capable of delivering flexible, value added, high speed and high bandwidth services directly from the optical (WDM) layer. Different applications/end users need different levels of fault tolerance and differ in how much they are willing to pay for the service they get. The current optical networks are capable of providing either full protection in presence of single failure or no protection at all. So, there is a need for a way of providing the requested level of fault tolerance (reliability) to different applications/end users. We choose the reliability of a connection as a parameter to denote the different levels of fault tolerance. In this paper, we consider the problem of dynamically establishing reliable connections (R-connections) in wavelength routed WDM optical networks. We develop an efficient algorithm to select routes and wavelengths to establish an R-connection with a specified reliability guarantee, in a resource efficient manner, using primary-backup approach. In our scheme, we provide partial backup lightpaths for varying lengths of the primary lightpath to enhance the reliability of the connection. The length of the primary lightpath for which the backup lightpath is provided depends on the reliability required by the application/end user but not on the actual length of the primary lightpath, network topology, and design constraints. We present the initial experimental results which suggest that our scheme is attractive enough in terms of resource utilization and average call acceptance ratio.