Abstract: Wavelength division multiplexed (WDM) ring networks that groom tributary traffic streams are considered. To efficiently utilize bandwidth, traffic may be rearranged by "bridge and roll". The WDM networks are nonblocking under a nonstatistical traffic model. Under the model, the amount of traffic over each fiber link is bounded, and the amount of traffic terminating at each node is bounded. Ring networks are presented that have significantly lower numbers of line terminating equipment (LTEs) compared to a ring that has only opaque nodes. In one case, the reduction can be as much as 44%. Bounds on the number of bridge and rolls to accommodate a new traffic are given.