Drive to the Cuba Gulch Trailhead from Lake City; or as far as your vehicle can make it. The further you drive the shorter the climb. From the Cataract Gulch Trailhead it is 14 miles roundtrip. From the Cuba Gulch Trailhead it is 7.2 miles roundtrip. From high parking in Upper Snare Gulch it is 2.4 miles roundtrip.
To get within striking distance of "American Peak" follow the Snare Gulch Road from the Cuba Gulch Trailhead. After Ascending the Snare Stairs (better to walk them in my opinion but then I dislike 4 wheel driving). From the above timberline Jones Mountain is the unimpressive hump at the head of the drainage and "American Peak" is the ridgeline to the right. From here the actual climb begins.
From where the 4 wheel drive road emerges from timberline the routes are obvious. The ascent of "American Peak" requires leaving the road to cross rolling tundra to the east. Aim for the more solid looking portions of "American Peaks" south ridge (testy scree abounds around here). Once on the ridgeline proper the route becomes obvious and "American Peak's" summit is easily gained. From the summit of "American Peak" there is aspectacular view of Jones Mounntain.
To continue the traverse of "American Peak's" complete summit ridge follow the southwest ridge, contouring around the couliors and minor summits. This traverse has a use trail and is quite enjoyable. As one approaches the "American Peak"-Jones Mountain saddle the views of Jones Mountain become much more impressive. This saddle is where the "American Peak's" West Ridge Route gains the upper slopes. Go south down scree covered slopes to get back into upper Snare Gulch. Stroll across the grassy basin to rejoin the road.
It is possible to continue on from the "American Peak"-Jones Mountain saddle to climb Jones Mountain
(0.8 miles distant) and Niagara Peak
(1.4 miles distant).
Just working legs and an appetite for alpine beauty. Winter would be different. If you are willing to ascend Snare Gulch in the winter the actual climb should prove easy. Surviving the Snare Gulch approach would be the hard part.
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