A method is performed at a router configured to perform Bit Index Explicit Replication (BIER) for forwarding of multicast packets in a network. The method includes, upon receiving a multicast packet of a multicast flow, accessing flow mappings in which multicast flows are mapped to fixed accounting values corresponding to the multicast flows. The method further comprises generating a BIER header for the multicast packet by encoding a multi-segment entropy field of the BIER header with (i) a variable entropy value for equal-cost multi-path (ECMP) load balancing, and (ii) a fixed accounting value among the fixed accounting values that is mapped to the multicast flow in the flow mappings. The method also includes encapsulating the multicast packet with the BIER header to produce an encapsulated multicast packet, and forwarding the encapsulated multicast packet.