We propose an on-line wavelength assignment algorithm for multi-fiber WDM networks, in which lightpaths are established and released dynamically. For a given number of fibers per link and number of wavelengths per fiber, the algorithm aims to minimize the blocking probability. It may also be used to reduce the number of wavelengths required for a given tolerable blocking probability. Simulation results show that our wavelength assignment algorithm performs better than other previously proposed algorithms (in the cases we studied). As the number of fibers per link increases, the benefit of having wavelength converters decreases dramatically, and the performance improvement of our algorithm over others increases. Our results also show that in case a preferred path is not available, rerouting along a node-disjoint backup path can significantly reduce the blocking probability.