I stepped out of the outhouse near the end of the Grinnell Glacier Trail and found myself staring at a bighorn sheep standing in the path. I was stuck.

The only way back to the main trail was blocked by a five-foot tall, 150-pound wild animal with a head built for battering. Lodgepole pine and other high-elevation trees made up a small grove around us, with an understory of various shrubs that made an off-path escape unappealing.

Thankfully, they’re not aggressive beasts, and I kept my distance. I took a step or two to my left, positioning myself behind a low stone bench (like that would thwart a charge) to wait him out.

In reading up on the fauna of Glacier National Park—mostly about how to avoid bears and spot moose—I took note of the advice to avoid eye contact with the animals. So I looked over toward Casey, a bemused look on her face as she stood in a clearing along the main trail.

And there we stood: Me watching my wife, my wife watching the bighorn, the bighorn watching me.

The sheep gave up first. Before long, he decided he’d had enough and turned to his left, stomping off through the bushes to find something better to do than contemplate another visitor. I rejoined Casey and we began to make our way back down to Lake Josephine.

We’d begun our day with breakfast at the Ptarmigan Dining Room in Many Glacier Hotel before heading outside to the dock on Swiftcurrent Lake to catch the first of two shuttle boats that would cut off about 3.5 miles of hiking.

We boarded Chief Two Guns for a 9:00 a.m. departure, disembarked at the western end of the lake for a quarter-mile walk up and over a hill to the eastern edge of Lake Josephine, then boarded the Morning Eagle to cross this second lake.

Stepping off the boat, we were on our own. A guided tour took several visitors on a flat hike through the forest to Grinnell Lake. We headed around Lake Josephine to pick up the Grinnell Glacier Trail, one of the most popular treks in the park.

Up ahead on the trail was a guided tour group that had a half-hour head start, because the guided option is only available if you take the first boat of the day. Given the choice, we’re more explore-at-our-own pace hikers, and for this walk, we wanted to experience the glacier without the cacophony of a group two dozen strong that arrives all at the same time.

As we met the trail and began the climb, we could spot the group when turns and switchbacks opened up the view ahead, and it couldn’t have taken us more than a mile to pass them. Our goal was to reach the glacier in time to take it all in before they arrived—at what I’m sure must be considered Grinnell Glacier’s rush hour.

(It should be said that we’re not against guided tours. We’ve taken advantage of ranger-led group outings from time to time, including later during our Glacier National Park visit, but this was one instance where we wanted to enjoy the park and the hike at our own pace and in our own space.)

A little over three miles from the dock, we reached the grove of pine, fir and aspen, with its low wooden benches and a sign for the pit toilet. A small group of people crowded around a bush, and as we approached, we could see why: The bighorn sheep I’d soon face off with was grazing on the green leaves.

One tourist took a step into the brush, turned to face his outstretched arm, and snapped a selfie some six feet from the horns.

I got some photos—from a reasonable and safe distance—before we ticked off the last quarter-mile to reach the edge of Upper Grinnell Lake and the glacier on the opposite side. We shed our packs, enjoyed a snack and some water, and just sat there, watching the ice.

I had the good fortune of taking video just as a small chunk of the glacier calved off and splashed in to the frigid, aqua water.

It was perfect. We had plenty of space to ourselves, the other hikers spreading out, seeking their own private moments. We were able to get a picture of the two of us and return the favor for a mother-son couple before we decided to turn back.

Our timing was spot-on, because as we crested the hill to pick up the trail heading back down to the rest area, the tour group was just beginning to arrive. We’d had all the time we needed.

After spending my quality time with the bighorn, the walk down was a breeze. The sun warmed us as we descended the 1,800 feet we’d climbed up earlier, bringing us back down to the shores of Lake Josephine—itself 4,800 feet above sea level.

Back at the dock, we settled in to wait for the return trip on the boats. Coming over, the operator had told us of the return times, stressing that the last return boat of the day would depart at 5:15 p.m. We made it back in time for the 4:15, with no more than half a dozen people before us.

If you, like us, would expect lovers of the outdoors—serene national parks visitors—to organize themselves and line up in an orderly fashion to board the boat when it arrived … you would, like us, be disappointed.

As other folks returned from their hikes and settled in to wait, I took note of the six or so who had been there before us, but as the group grew, order disappeared.

When the boat arrived and the attendant came to the foot of the dock and told us he could see that there were more people waiting than would fit, he suggested that anyone who wanted to walk the 2.5 miles back to the Many Glacier Hotel do so.

Then he left it up to us to decide who boarded first. Any remaining sense of order immediately vanished as people surged for the dock.

“Come on, people!” someone near the front exclaimed. “You know who was here before you!”

That seemed to shame some folks into taking a step back, and we were able to board (as we should) for the ride back. Had I known there would be so little organization and guidance—and I do think the boat operator could enforce a more orderly procedure—I’d have suggested we walk back to the hotel. But I was the one who decided I’d rather rest and wait for the boat.

But that was the only frustrating moment in an otherwise enjoyable day. We made it back to Many Glacier by 5:00 p.m., ordered a couple of cocktails at the bar, and found a pair of unoccupied chairs out on the balcony. We put our feet up and sipped our well-earned drinks as the sun sparkled off the small whitecaps of Swiftcurrent Lake.