ESTEEMED COLORADO alpinist Lou Dawson calls mountaineering "a social voyage that cements friendships—or reduces us to the raw basics of negotiation, leadership, and conflict." Given our four competitive personalities, which find their full expression every night in vicious billiards games, friction is bound to happen, and it rears its head shortly after four o'clock on day 11, in a tiny Italian hamlet with the flatulent name of Purtud.

Lance and Beej, as is their hypercompetitive-skinny-guy wont, reach the bar first, and Lance orders two beers. When Lee and I arrive, expressing shock that Lance didn't buy a round, he says, "I didn't know you wanted one."

"I didn't know the sun rises in the east," I say.

And what's Beej's deal? I know Lee wants him to "pop" on film, but all those greens and yellows? He looks fruity, like Sprite's mythical "lymon." As for Lee, who sports a writhing lip caterpillar, I refrain from telling him that Magnum, P.I. went off the air 20 years ago.

We're headed back to France, approaching Western Europe's highest peak, 15,771-foot Mont Blanc. Also, back to cheese that arrives in tartiflette, rather than a calzone the size of a cat. We manage to squish into the three-stage Funivie cable car without impaling an infant on an ice ax. At the apex, we get out and push through a beaten metal door painted with green, white, and red rectangles on one side, and blue, white, and red on the other: the flags of Italy and France, respectively.

With giant needles hovering all around us, we engage the world's longest, most famous run: the Vallée Blanche, a glacier that courses between cliffs and seracs for 13.7 miles. To ski the Vallée Blanche is to swerve forever around crevasses and fallen novices, who flock here en masse despite their talent level. But, says Beej, "this is the best snow of the trip! This is sweet. Sweet cream."

Most Vallée Blanche descents stop at Montenvers, where a train waits to trundle skiers the final 20 minutes to Chamonix. Between the glacier and the train, though, is a 280-step staircase, which is a fun place to watch scores of Euros simultaneously reconsider their pack-a-day cigarette habits.

The next day, we take a high-speed quad up Flégère, one of six ski hills around Chamonix, and then sweat our way up a frighteningly steep slope. From the ridge, skiers and snowboarders sporadically drop down, going right or left, but we charge straight ahead, milking elevation, skiing across more than down, till halted by a creek. Then a chug of water, re­attachment of skins, and more of the chunka-ssss-chunka-ssss of our bindings hinging and skins greasing up across the snow. We soon reach a snowfield 200 feet below our objective: a humpy cornice atop another long ridge. Problem is, it's hot, and we worry that tendrils of bonded snow will melt and drop a ten-ton chunk of cornice on our heads. Should we turn back? We should go for it.

We stretch out, 8,043 feet above sea level, with glorious views of Mont Blanc, Les Grandes Jorasses, and l'Aiguille Verte. In the distance, the shore of blue Lake Geneva sparkles. We snarf dark chocolate and snap photos. No wind blows. We plop our heads down and doze. "This is the most perfect place of all time," Lee raves before conking out.

Later, we ski silky hero snow meandering to the right. For a moment we seem lost, but we gain a rollover and spot a cluster of barn buildings: Chalets d'Anterne, a popular summer stop for hikers. In April, it's empty. After 13 days among the Alps' teeming masses, we suddenly have an entire beautiful European valley to ourselves. Mon dieu.