This one isn't for the faint of heart. Inexperienced rock climbers, stay away: there are some potentially dangerous spots (especially a huge keeper sinkhole, supposedly avoidable by scrambling). It will take at least a full day the first time through, and involves lots of rappelling, some free hanging, and swimming. Bring a wetsuit; the air is warm, but the water is always cold.
The rewards are beautiful, water-sculpted rock walls, long descents, lots of solitude, and a gorgeous, fulfilling canyoneering/climbing experience.
A pickup car at Call of the Canyon Picnic Area (34.990681, -111.74242) is strongly recommended to avoid a long hike after the already grueling day. It's a long drive from there to get back to the other car.