We propose a new scheme for multicasting in a binary tree that combines packet self-replication and routing in a space-division ATM switch. We revisit Law and Leon-Garcia's approach for packet self-replication and routing [15]. Then we propose a new packet self-replication and routing scheme using only 2(b) address bits for a b-level binary tree. This method, when applied to a unique 3-dimensional ATM switch architecture [19], constitutes an optimum combination of packet self-replication and routing for multicasting in a continuously expanding self-routing space-division switch.