In this paper, we analyze the performance of WDM networks with traffic grooming capabilities supporting low-rate circuit-switched traffic streams. Traffic grooming in WDM networks collectively refers to the multiplexing, demultiplexing and switching of lower-rate traffic streams onto high capacity lightpaths. Networks which perform grooming only at the OADMs present in the nodes are referred to as Constrained Grooming Networks. Networks whose nodes switch traffic streams between wavelengths and perform grooming at the OADMs are referred to as Sparse Grooming Networks. Given the network topology, the traffic matrix and the node locations of grooming and traffic stream switching, we present an analytical model, using link-independence and wavelength-independence assumptions, to calculate the blocking performance. We illustrate the benefits of sparse grooming over constrained grooming in the mesh-torus and ring network topologies, using both simulation and analytical results.