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Do you guys strop over the stamp often found on strops? My Kanayama has quite a large one at the top near the hardware and I always wondered if it was messing up the edge. On the other hand, my Tony MIller has quite a big one.
Maker's marks have always been on the face of strops, or on the handles on short models (visible). Given that the modern strop tends to be 10 - 15 cm longer than most vintage models (many barber stops excluded), it would seem that there is ample stropping room. One could also see it like this: with the speed stropping is performed, how likely is it that the visual cue of a maker's mark prevents one from flipping the razor onto the hanger or handle?
I believe that Tony Miller's mark can also be stropped over with no problem.
If you want to "avoid" stropping over the mark, then...
If you strop vertically, then raise the height of the strop.
If you strop horizontally, then move the strop further to the left or right depending, if you are left or right handed.
I can't say that I am 100% sure, but I believe that the logos serve two functions: as ornamentation and as demarcation markers that aid in preventing the user from cutting themselves near the handle or damaging the razor near the hanger. Personally, I would just try to avoid bringing the razor over the logos, though I am sure I do it on occasion.
My stroke continues almost to the very end of the strop at the handle end. A bit shorter on the hanging side. But.... I tend to be in the process of lifting the edge off the strop on the towards stroke and turning the blade ready for the away stroke. On the away stroke the blade moves over the logo before the edge hits the strop.
To clarify about stropping over a mark: A branded mark makes a depression in the surface. Unlike many of the vintage (and some contemporary) marks, which use a foil transfer with a minimal depth difference, one should not worry about stropping over these. Not that I would worry about 30 mm of stropping length...