Wavelength division multiplexed (WDM) routed optical networks represent the direction towards future high-capacity wide-area network applications. A serious issue in WDM-routed networks, though, is light-path allocation which requires a combination of optical routing and wavelength assignment. While near-optimal-routing and wavelength-assignment algorithms aimed at minimizing network wavelength requirements have been reported, the practicability of wavelength-routed optical networks depends on the number of wavelengths required to satisfy a given traffic demand. In this paper, we proposed two symmetrical routing and wavelength-assignment methods for optical networks with a Grid or ShuffleNet physical topology. Here, we consider the case of non-adaptive wavelength routing systems, where the operations performed in nodes are independent of the network traffic load. In this case, the routing differs somewhat from that in adaptive routing networks where the routing function may produce different results at different times. The path followed by a wavelength never changes in non-adaptive wavelength-routing networks. When all N(N-1) node-pairs are to be connected, our methods lower the wavelength requirement to (or close to) its calculated minimum. Symmetry is a basic feature of both these regular topologies, but there are differences in the features within the topologies. Our goal has been to try to make use of the symmetry, and the differences in the native symmetry features, of these regular topologies to yield a lower wavelength requirement.