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USA custom razor maker Robert Williams makes just that. Calls it The Purist and a lot of guys seem to like it. I think Charlie Lewis might make one, Mastro Livi ....... they are out there and, matter...

Just IMHO, the ability to fold the handle, straighten it, or holding it somewhere in between when I'm shaving is mighty handy. Full disclosure, I've never had a fixed straight razor, or shaved with...