Multicasting in WDM core networks is known as an efficient way of communications in high-speed multimedia pplications. However, costly and complicated fabrication prevents multicast capable switches (splitters) from deploying in the proposed architectures. Besides, in practical routing cases, the state of the network is given by a directed graph. Accordingly, this paper investigates the multicast routing without splitters in directed asymmetric topologies. The objective is to minimize the number of wavelengths used and then find the best cost solution among those requiring the same number of wavelengths. In the case of no splitters, a set of light-paths starting from the multicast source covering all the destinations is known as the traditional solution. In this paper, we introduce two new concepts namelylight-trail based hierarchy andlight-path based hierarchy, and develop two ILP formulations for them. Theoretical analysis and simulation results show that the optimal solution is a set of light-trail based hierarchies. Particularly, our light-trail based solution achieves fewer wavelengths required (up to 21.95% saved) while keeping slightly lower cost (up to 3.79% saved) compared to light-path based solution.