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. In practical routing cases, the state of the network is given by a directed graph. The paper investigates the multicast routing without splitters in directed asymmetric topologies. The objective is to minimize the number of used wavelengths and if there are several solutions, choose the best cost one. We show that the optimal solution is a set of directed light-trails. The problem is NP-hard even in symmetric digraphs. An efficient heuristic is proposed to minimize the conflicts between the light-trails, and so to minimize the number of used wavelengths. The performance is compared to existing light-trail based heuristics and the four our algorithms provide a good solution with a few wavelengths required and a low cost.