I made a strop last night, I'll post a pic after work.
edit: here it is. Tandy leather 3 inch wide 50 inch length for around 35 bucks, I cut it in half then folded the top over and sandwiched the fabric. Hole punched and riveted the pieces together. The bottom I cut a 3 inch piece and folded it over, hole punched them then sandwiched each strop to hold the D ring grip. For a swivel I bought a piece of leather lacing and just tied it on. The remaining hunks of leather I will use to make board strops for pastes.
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Scookum
I like your idea of sandwiching the fabric on the back side of your strop. Very cool idea.
That eliminates the need for putting a handle on the fabric. Again, cool idea.