Multicasting in WDM core networks is an efficient way to economize network resources for several multimedia applications. Due to their complexity and cost, multicast capable switches are rare in the proposed architectures. The paper investigates the multicast routing without splitters in directed (asymmetric) graphs. The objective is to minimize the number of used wavelengths and if there are several solutions, choose the lowest cost one. We show that the optimal solution is a set of light-trails. An efficient heuristic is proposed to minimize conflicts between the light-trails, and so to minimize the number of used wavelengths. The performance is compared to existing light-trail based heuristics. Our algorithm provides a good solution with a few wavelengths required and a low cost.