We’ve all crowded onto the South Rim of the Grand Canyon to snap that unforgettable photo, only to find that the most memorable thing is bumping elbows with a Clark Griswold-type sporting a huge sombrero.

Welcome to our national parks. In 2002, 18 of them stockpiled at least one million visits each, making them feel more like a New York subway ride than a back-to-nature experience. You endure bumper-to-bumper traffic, only to hear cell phones ringing as Old Faithful erupts. Even in the middle of nowhere, space is a commodity: Getting that snapshot of the Grand Canyon means elbowing aside over four million people; cruising through the Smoky Mountains involves competing with a whopping nine million.

Visitor numbers alone don’t tell the whole story, though: there are, after all, almost 81 million acres of park to accommodate everyone. A couple million people in Alaska’s Wrangell-St. Elias wouldn’t matter much—the park is spread out over 13.2 million acres. But Maine’s Acadia is allotted only 48,000 acres; the 2.5 million visitors per year have to endure an average of 54 people per acre. And if you really want to talk sardines, check out Arkansas’s Hot Springs ; with 1.4 million visitors squeezing into 5,550 acres, there were—get this—282 people per acre.

Of course, weather’s key: Who visits North Dakota in January? According to stats from Theodore Roosevelt NP, hardly anyone. Big surprise. But the 672 hardy souls who visited in January 2002 ballooned to 120,000 by peak season: August. Down south, it’s the opposite: The 32,000 who jammed into Texas’ Big Bendin March dwindled to a mere 16,000 by steamy July.

How do you escape the teeming masses? Head to one of America’s lonely parks and snag some of your own space. We did the math to give you an idea how much acreage you’ll have to yourself. Of course, the majority of these acres are in already-lonely Alaska, but a couple parks may just surprise you. So find your peace here, in places with space enough and few enough numbers to make them gloriously lonely.

Gates of the Arctic National Park, Alaska

The winner, by a long shot, is Gates of the Arctic, sprawled out over the Brooks Range in north central Alaska. An untouched area that avoided American and European influence until the 1880s, Gates will be tough for you to reach, too, since its glaciated valleys mean you have to fly in. And, with snow possible at any time of year, you could wait for days for decent weather to get out. How lonely is this place? Even the park service says that “it may be weeks before you encounter another person.” Weeks! It ain’t easy living. The winter brings temperatures as low as 50 below, and summer months mean rain and mosquitoes. The payoff includes stunning scenery, warm springs, great fishing, and wildlife spottings (bears, moose, and eagles, to name a few) all to yourself.

Wrangell-St. Elias National Park, Alaska

With 13.2 million acres, it’s safe to say you’ll have plenty of room to spread out in Wrangell-St. Elias . A day’s drive east of Anchorage, Wrangell is not only America’s most mammoth park (it could hold six Yellowstones), but North America’s largest assemblage of glaciers, and its highest concentration of 16,000-foot-plus peaks. Facilities? Sure, if you like small emergency cabins with bunks and wood stoves (potential saviors, though, since snow could come any time of the year). Don’t expect maintained trails, but make the effort to get above tree line—it’s the best place to see the wild sheep, bear, caribou, moose, and mountain goats. The coastal area adds sea lions, harbor seals, sea otters, porpoises, and whales.

Kobuk Valley National Park, Alaska

Like many Alaskan parks, getting to Kobuk Valley, in northwestern Alaska, is tough (and expensive), since you have to hail an air taxi in Nome or Kotzebue. And don’t expect much in the way of amenities once you get here: Trails and roads simply don’t exist within the park’s 1.7 million acres. Still, hardy outdoors types are drawn by hiking, biking, dog mushing, fishing, boating, and wildlife viewing. Don’t squeeze in too much, though: The scenery is gorgeous, since you’re surrounded by two mountain ranges that give protection to the central part of the Kobuk River. Go play among the many dunes, a result of glaciers grinding and carrying tons of sand to this valley.

Katmai National Park, Alaska

These days, July’s the only time people venture to Katmai in any kind of mass. But this park, on Kamishak Bay in southwestern Alaska, was a hotbed of activity in prehistoric days, and the frozen tundra has allowed for North America’s highest concentration of prehistoric human dwellings (with about 900). Getting around is a struggle: Not only do you have to fly in, but you have to fly virtually everywhere. Brooks Camp, the only fee-based camping area, is about 30 air miles from park headquarters in King Salmon. Once settled, though, you’ll be surrounded by Katmai’s stunning beauty, 14 volcanoes, and rivers, where bears congregate for the popular fish feast during salmon spawning season. Want to get in on the fishing action? Do it—it’s world-class.

North Cascades National Park, Washington

Forget about Glacier National Park. If you want ice mounds all to yourself, head to North Cascades, in Washington’s Canadian borderlands. You’ll find 318 glaciers, or about 60 percent of the total glacier-covered area in the contiguous states. The loneliest park in the lower 48, North Cascades is very accessible; a highway runs right through it, and you’ll find lots of campsites, as well as a couple resorts. In between it all live cougars, black and grizzly bears, mountain goats, and gray wolves. There are also valleys worth of western red cedar and forests dense with Douglas fir, with enough breaks for sweeping views of those alpine glaciers.

Isle Royale National Park, Michigan

Adrift in a corner of Lake Superior, seclusion reigns on the archipelago that makes up Isle Royale, officially part of Michigan but closer to Thunder Bay, Ontario, than the Spartan state. Visitors need to fly or ferry in, and marine radio’s the only connection to the world. The park service encourages further solitude by suggesting that people “refrain from group games like tag, which often lead to extra noise,” but it’s pretty quiet already: A full 98 percent of the park is designated wilderness area. You can check out the lighthouses, fish for native lake trout, and explore abandoned copper mines. Most people come in July and August, of course, and so do the mosquitoes, black flies, and gnats. Shoot for spring or fall.

Glacier Bay National Park, Alaska

You say you really need some space? Is 1.6 million acres enough? In December 2002, the 3.3 million acres in Alaska’s Glacier Bay were divided among a whopping 71 visitors. Stretching north from the Inside Passage and bumping up against upper British Columbia, the park’s a birder’s paradise, home to more than 25 percent of the total number of North American species. Other wildlife? You bet: Sea lions and humpback whales follow the ebb and flow of the glaciers and deep fjords. Kayaking is king here, since steep rocky cliffs with dense alder thickets make hiking difficult. Ferries run only from May to September; the rest of the year you’ll have to fly in. Accommodations? Expectedly sparse: There’s just one campground, and Glacier Bay Lodge is open only in the summer. Another caveat: The weather ain’t great, so don’t forget your canvas tent!

Denali National Park, Alaska

Famous Denali has held onto its top ten spot despite becoming one of Alaska’s most accessible parks. The cruise-ship crowds come by the busload, and you can get here by car, train, or shuttle, from Anchorage or Fairbanks. But its six million acres have helped absorb the ever-growing human population, and the infrastructure has grown to support everyone, too, with many campgrounds and several luxury resorts. Just about every sport is popular here: hiking, biking, bird-watching, fishing, skiing, and (with America’s highest peak inside its boundaries) mountaineering.

Death Valley National Park, California

You don’t have to brave the Alaskan winters to find solitude. A whopping 900,000 people poured into Southern California’s Death Valley in 2002, but with almost 3.4 million parched acres, the numbers didn’t matter much. Of course, in this very accessible playground (just two and a half hours from Las Vegas), the danger is excessive heat; summertime mercury can clear 120 degrees. You’ll find plenty of great hiking and camping among the dunes and cracked earth; just be sure to use a four-wheel-drive when braving the backcountry. Accompanying you through ghost towns and the lowest point in the western hemisphere (282 feet below sea level) will be bats, gophers, porcupines, and, of course, tons of reptiles.