ultra-thin case?

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So I have now acquired two TPU cases and evaluated a hundred more.

I did a search and read all of the threads about cases on this forum. Maybe someone knows of something new that's not in these threads.

What I really am looking for is a hard case/cover that is very, very low profile like the ultra-slim ones that are available all over for iPhones. The TPU cases add probably 2mm of bulk in every dimension to the phone, and I am looking for something that is more like under 1mm of extra bulk in any dimension.

Also it'd be nice for a case to be easy to get on and off of the phone since I have to remove it to put the phone in the mount on my bicycle.

Anyone seen anything like this?