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.