A lot of your water treatment needs for the Rincon Mountains depend on 1) the time of year and 2) where you are headed. I average three weeks a year in the Rincon Mountains in all seasons. The worst time for finding water sources is in late spring and early summer just before the summer rainy season starts. Late fall can also be a bit dry. Knowing the water sources is a big help but hard to do if you are not a local.

As Old Ranger stated, most of the approaches to the Rincon high country are dry even in the wet times of year. Most hiker traffic is on the Tanque Verde Ridge trail to Manning Camp. The first relatively reliable water on that trail is at Juniper Basin (8 uphill miles) and that often dries up in late spring. Manning Camp (16 miles) was dry for a while last year; it is usually reliable. So, plan on taking plenty of water for the first day and inquire about water status at the Visitor Center before you start hiking; you can do this by phone.

Based on my personal experience, I would not use a gravity filter in the Rincon Mountains. A lot of the available water sources are hard to get at and small. They occur in small pockets well below the general surface -- Think of seeing water at the bottom of an 18" deep, 4" wide gap between large boulders. The water sources can also be quite biologically active. This means: 1) scooping water out to put into a gravity filter can be problematic at best and; 2) you need a filter that is easily back-flushed or otherwise cleaned.

A filter that can draw water up from an otherwise inaccessible source is a definite plus in the Rincon Mountains as is one that can easily and quickly be field cleaned. I have had to clean my filter after pumping less than a liter.

Also, even after filtering, some of the water sources can yield some pretty foul-tasting/smelling water. I frequently add a Micropur tab to my filtered water just to make it taste and smell better. It really helps.

I use an old MSR Sweetwater for my Rincon trips. I am sure that there are many others that meet the above criteria but I bought the MSR some time ago and have never felt the need to replace it. But, any filter that can be cleaned and that can draw water up from a sunken source will be more useful than a gravity filter.
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May I walk in beauty.