Mesh-based multicast routing protocols in Mobile Ad Hoc Networks (MANETS) allow data to be sent to all the members of a network through multiple paths. As a result, these are more efficient in comparison to tree-based protocols, provided the links remain stable over a period of time. Otherwise this redundancy results in a waste of energy on links that eventually die out before complete data transfer. In this paper, a new protocol SLIMMER (Stable Links in Multicast Mesh and Energy Efficient Routing) has been introduced, which overcomes this problem by considering energy efficiency of the nodes as a decision criterion to improve link stability. Its performance has been compared with the popular mesh-based multicast routing protocol PUMA. Results show that SLIMMER outperforms PUMA in terms of packet delivery ratio (PDR) and energy consumption, under conditions of varying number of nodes, mobility, and simulation time.