“I’ve had moose tags,” Dieruf said. “But I’d trade all four for one sheep.”

The second way to secure a chance at a wild sheep is to spend a lot of money. While residents of Alaska and those in Canada generally can hunt sheep within their own state, province or territory, nonresidents are required to hire a registered outfitter. The laws of supply and demand push the price of hunting a Dall’s up to about $25,000 and a Stone’s sheep to about $50,000. Hunts in Mexico, through outfitters or private landowners, can reach $100,000.

A wealthy few go beyond that. They bid on exclusive permits that are auctioned off annually to raise money for states, provinces and Indian reservations, seeing their lavish spending as a charitable donation, a tax write-off and a chance to capture one of hunting’s premier trophies.

“Some rich people are into yachts or floor tickets to the Lakers,” Burns said. “Some sheep-hunt.”

What they are not buying is an easy trophy. Sheep live in steep and treeless terrain, above the timberline in the mountains or in the rugged hills of the desert. Sheep hunts can take hunters into places few humans have gone, and can include weeks of trekking and stalking.

“For the true hunter, you can’t buy them behind the fence,” Kronberger said. “You have to climb the mountain. The fat, rich guy is going to have a much harder time. Anybody can kill a bear if they sit on the beach or along the stream long enough. I could take a guy in a wheelchair and get him a bear. You can go and get your deer, get your elk. You can’t do that with sheep. You have to go and get it.”

All that can be hard for non-hunters to understand. Those who have trophy rooms filled with a wide selection of mounts, like Corrigan and Kronberger, said that guests are rarely attracted to the sheep at first, instead taken by the more glamorous and fearsome animals. It is like a litmus test for hunting credibility.

“If I brought 1,000 people into my trophy room, almost all of them would go to the bears and say, ‘Wow, look at the bears,’” Kronberger said. “Only a few know to go to the sheep — the other sheep hunters. Half the time, people call the sheep a goat.”

Bidding at the ‘Sheep Show’

Brendan Burns sat in a padded stackable chair in the Tuscany Ballroom of the Peppermill Resort Spa Casino in Reno, Nev. It was a Friday night in January, and there were about 1,000 people sitting at 100 round tables, having just eaten the one entree offered: steak. A convention of hunters was no place for a vegetarian option.