I learned a lot from the answers to your question. I find that the more I travel, the more electronic I become. However, there are some things that I prefer to have in hard copy.
Those and some other things go in the safe if where I'm staying has one. When it doesn't or I'm on the move, that stuff is in my carry-on roller bag or spinner. I check nothing.
My roller and my spinner both have u-shaped handles. Both also have a zipper in the liner to provide access to the mechanism for repairs. That area is my favorite place to put any copies or paper that I don't need right away.
I hate wasted space, so I pack odd things around those rails, filling up the spaces to make a flat platform for the rest of my packing after I zip the liner closed. Really flat and thin things, like copies, can actually go between the rails and the reinforced backs of those bags. I tried filling in those spaces with the liners zipped, but it didn't work because the liners are slightly smaller than the space itself.