Within the U.S. Grand Circle area, where is the number of daytime trail permits limited?

Question

Within the U.S. Grand Circle region (very roughly Las Vegas NV /Provo UT/Aspen CO/Santa Fe NM/Phoenix AZ), for what trails are the number of permits issued limited considering day use only?

I am aware of the Coyote Buttes area in Vermillion Cliffs National Monument near Page, Arizona (lottery-based for Coyote Buttes North including The Wave, and based on who applies first for Coyote Buttes South, but the Paria Canyon in the same area has no daytime limit). Are there other areas where the number of daytime permits is limited for day-time use?

For the scope of this question, I am not considering trails with a limited number of overnight use permits, nor am I considering trails that require a permit, but do not limit the total number issued. I am also not considering trails where access is only permitted with a guide, such as Antelope Canyon or areas in Canyon de Chelly National Monument.

Answer 1

The Subway, Zion National Park

Within Zion National Park, for most of the year, day-use permits are required for The Subway and Mystery Canyon. They are awarded by advance lottery, or by last-minute drawing 7–2 days in advance. The lottery is not required during the low season (roughly November through March).

This applies either for the full canyoneering route, or for non-technical hiking up to the point where canyoneering skills and equipment are required.

Source: Wikimedia Commons, CC-BY-SA user “True God of War”

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Moon House, Bears Ears National Monument

Within Bears Ears National Monument, the Moon House ruins are limited for day visits, with apparently up to 36 permits per day issued. Permits are available through BLM.

Source: Matt Peeples via Wikimedia Commons (originally on Flickr), CC BY-NC.