In a WDM optical network, the bandwidth requirement of a customer's connection can vary over a wide range, and many of these connections could have a capacity that is much lower than the capacity of a wavelength channel. Efficiently grooming low-speed connections onto high-capacity wavelength channels can significantly improve the bandwidth utilization and minimize the network cost. Our research shows that it is not necessary to have traffic-grooming capability at every network node. We call a network which has only a few grooming nodes to be a sparse-grooming network. Through proper network design and traffic engineering, it is possible for a sparse-grooming network to achieve similar network performance as a network which has grooming capability at every node. We investigate the problem of designing such a sparse-grooming WDM mesh network. The problem is mathematically formulated and several design schemes are proposed. Illustrative numerical results from the mathematical formulation as well as heuristics show that, by properly choosing the grooming nodes, a network with sparse-grooming capability can achieve good network performance and the network cost can be significantly reduced.