Just past crowded May Lake is Tuolumne Peak, a short couple of miles of off-trail walking and scrambling, but feeling much more remote, with stellar views of the Cathedral range, Half Dome, and north toward Hetch Hetchy.

There are technical routes on this peak but from May Lake it's a walk-up to the true summit, with a beautiful but short third and fourth class ridge-walk to the western summit.

Secor's directions go something like "Tuolumne Peak is class 2 from the north end of May Lake" which is true, but more specifically...

From the May Lake trail head, follow the trail past the High Sierra Camp, past May Lake, then leave the crowds behind. Shortly after the trail starts downhill north of the lake, leave the trail heading cross-country northward below cliffs to the west. Once you hit the open slabs (small streams in the runnels in spring), head northwest toward a forested north-south valley. In this valley you'll find a really cool old trail, with well-engineered switchbacks. Not sure what it used to be, but it's still in good shape. Follow this trail til it peters out and continue north through delightful meadows. At the saddle, Tuolumne Peak is finally visible to the north. Pick a path to the summit.