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For a great alpine rock climb in the beartooths, The Tower of Innocence is hard to beat. It will give you 7-8 pitches of mostly 5.8 and 5.9 climbing, there are some short sections of 5.10 but nothing sustained. The rock quality is great and it is a short approach, by Beartooth standards. There are two other towers that lay next to Innocence, Tower of Poor Rock on the left and Tower of Incubus on the right. I have done routes on them as well and while the quality isn't as good as Innocence they are still worthy climbs. This summer I plan to link all three towers in a day, should be a great climb.
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Pitch 8
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Pitch 4
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Pitch 3
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Pitch 2
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At the start of the route, waiting to see if it was going to rain. It did rain, on pitch 8!