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I started out on a paddle strop and have been saying this all the time. The paddle doesn't flex like a hanging strop. Don't get me wrong, my hanging strops don't droop, but there is a bit of flex to them.
Moral of the story: If you tape while honing and use a paddle strop, you need to tape when you strop or the edge is more than likely not getting stropped.
This is why I actually added hanging strops to my stropping routine.
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That, shooter, is what I was wondering, too. I usually have a double-taped razor these days (the earlier ones were honed "naked"). I just add more pressure to make some "give" on the paddle strop and it works. But I do hear more imperfections being trued when I put a layer of tape on that razor and strop it (I only have paddle strops (2)). This is before and after refreshing an edge on a pasted paddle strop.
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I use the tape on the paddle strop because I don't see that much flex or give in the surface of the leather. The leather is quite thin and I think the tape keeps the bevel on the surface. I've had good luck doing this and like the results. To each their own.