The lightest cartridge I have used on moose was the 7x57 (with 160 North Forks) which worked fine, but a friend from Alberta has used the 6.5x55 on about 20 moose. He shoots them in the standard chest-spot, about 1/3 of the way up behind the shoulder, and they do the standard moose thing: stand around a little while and keel over. He has used a bunch of different bullets but I believe he mostly uses the 140 Nosler Partition, as it also works very well on Alberta deer (or about any other non-dangerous game on the planet).
