Tarptents are not much more open than the standard double-wall. They are fully enclosed tents. A better description is "lightweight single-wall tent" since "Tarptent" is a brand name.

I'm also a female who goes solo (except for the dog) and have no problems with me and my dog in a single-wall tent. I far prefer it to a double-wall!

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May your trails be crooked, winding, lonesome, dangerous, leading to the most amazing view--E. Abbey