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In this paper, we consider a circuit-switched optical wavelength division multiplexed (WDM) network that offers protection services to the connections established in the network. A dynamic traffic model, where connection requests arrive based on some stochastic arrival process, is considered. In earlier work, the notion of partial protection was introduced for a WDM network with sub-wavelength capacity allocation capabilities, as in TDM-WDM networks, for a dynamic traffic model. Here, instead of setting up a backup path with the same capacity as the primary, the backup path is established with capacity that is less than the primary path's capacity, where the amount of backup path capacity is specified by the user. Intuitively, this will reduce backup path requirements, thereby increasing the number of connections accepted. In (J. Fang et al., 2005), the mechanism presented attempted to provide the maximum available protection bandwidth while ensuring that the minimum backup requirements are met. However, this can still result in wasted protection bandwidth if failures do not occur. In this paper, we present a mechanism to further improve the performance of partial protection schemes for dynamic traffic. When failure occurs, the connection is carried on the backup with reduced capacity. However, the system tries to identify additional spare capacity on the same backup path, on either the same wavelength or a different wavelength. The objective is to increase the amount of backup capacity at the time of failure, so that the connection's end user does not see a noticeable drop in bandwidth allocated. We present a heuristic connection admission control algorithm that prevents backup contention that occurs when backup paths of connections affected by a failure contend (share) for resources. A detailed performance evaluation of the mechanisms for different network topologies and other system parameters is presented. For one of the cases studied, the connection acceptanc- e probability is increased from 95% to 99%, while providing nearly 100% backup capacity, when failure occurred. 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.