For those that are interested, I'm posting a tutorial of how I turn my little boxes. I'm sure there are many different ways to turn these and probably easier ways, but this is how I do it.
I started off by finding a chunk of dry mesquite, any wood would work, it just needs to be dry so the lid will keep a nice fit. I took it to the bandsaw and cut out a spindle blank that was about 2x2x5 (this one is a little bigger than the others I posted).
I then put it between centers and roughed it to a cylinder with my roughing gouge, then turned a tenon on the tailstock end (that will be the bottom piece).
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Then I mounted it in a chuck, brought the tailstock up and turned a tenon on the other end (this will be the top).
I took a pencil and marked where I would part off the lid. I usuall try to make the lid about 1/3 of the total length, but I just do it by eye.
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I used my thin parting tool and made a cut with the depth equal to what will be the thickness of the sidewalls. Then below that I start my parting cut. I part the lid section off and set it aside for later.
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continued....