There is lots of discussion out there about whether to use the split side or smooth side of leather for stropping. I have bench strops made both ways. I think Clay's photos have shown some differences in the results using each at 500X . There does seem to be a bit of difference at the microscopic level... not a huge one though. There is a thread listed in the WIKI where he shows photos of the differences with smooth side, split side cow leather and some horse but strops mixed in there. If you look at them, remember the magnification level when evaluting the difference.

With my horse butt strops, I took the "smooth" side down with sandpaper before even trying to use it. It was full of irregularities, fat deposits, scars and pores.
For those I started with 220 grit, then 400, then 600, then 1000 grit. It left a very fine nap, almost like buckskin and left the surface ultra flat. They work well though, better I am sure than had I not sanded them!! I probably spent a couple of hours on each 12 X 3" bench hone to make them to my liking... I do like the results I get using them with the full range of abrasives that I have!

So, to answer your question, I guess the level of damage you have to your strops will detemine how much material you need to remove to get the leather smooth. I guess no matter how much (or how little) you have to sand, you will end up with a different texture on the leather than you started with on the smooth side. I am not convinced that the difference in your edges will be even noticeable (except if you use very high magnification to view the edge). In fact, I find that the sanded leather holds my diamond sprays better then when they were not dressed by sanding.

Having said all of this, I have not bothered to mess with the strops until they were pretty beat up, or if I want to use them with a finer grit. When I say pretty beat up, I mean multiple slices and nicks... chattering accross the blade, black with blade steel powder, beat up.

As I first started with the strops, I did not understand how different they are from the stones.
Some of my movements produced some slices in the leather.
The term bumpy fits, it was not a smooth stroke they had become bumpy.
How to get them back smooth, how to remove the edges of the cuts and not destroy the strop?
Sandpaper on a hard surface came to mind.
I had 400 and 600 grit sandpaper used when I made hummingbird bands to polish the band edge so it
does not hurt the bird’s leg.
Taped the sandpaper to a bamboo cutting board and worked the strop back and forth.
It leveled the strop back out and it removed the edges around the cuts in the leather.
The strops were smooth as before.

So in my case I did not sand that much off. I cleaned them with alcohol, let them dry and reapplied the diamond paste, good as new.

Thanks guys. I will try sanding sometime.

I was surprised that the paste took to the WE strops as smooth as they were. I thought the paste would just smear off. I did load mine very lightly and the paste did smear easily by finger. But in the end it looks like they do retain the paste

Thanks for the advice everyone, I'm trying to be more cautious when stropping now so I don't slice it, but if it gets any worse I'll try to smooth it down like you guys mentioned

And no bad mouthing Chesty coreyschnaufer!

I am Army prior service so any time I get a chance to rib a toefl hunden I am required to take it.