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just go back and edit the original post (edit function is at the bottom of the post)

Double edge safety razor.

i agree, though even some of the really quite cheap soaps and creams do well, such as Arko, Palmolive etc.

Poor stretching, too dry lather, bad angle, old blade. These are all possibilities, unfortunately I can't tell you which is right.
I would try to keep as much the same as possible and change one...