Thanks for the detailed info. It helps clarify to many matters.
The two leathter strips are mounted together, back to back. So, if I am to strop on three sides (white compound, green compound, plain), aside from stropping on the two exposed sides, where is the third side? Do I just lift the top leather strip and strop on the inside of the bottom leather strip? It seems that the bottom strip will be really warp in that configuration, making it hard to maintain a consistent angle.
Sorry. Your original post read "Okay. I now have a leather strap. It comes in a pair and therefore four sides: two finished leather sides, one unfinished (rough) leather side, and one canvas side." I took this to mean that you had two smooth working surfaces, and one rough working surface. I'm now guessing that what you were calling a rough surface was just the back of one of the pieces.
Can you be a little clearer about your strop? Does it have a hanging loop at one end and a handle at the other, or are they loose pieces of leather? If you ordered it off the net, can you post a link to it?
If you only have two smooth leather stropping surfaces, dedicate one for white compound and one for green. Forget about using a bare strop in that case.
As far as distorting the leather, an unmounted strop needs to be firmly attached at one end, and pulled taut from the other. Don't press the knife so firmly that it bends the strop in use or you will convex the edge. This is one reason why I prefer mounted strops for knives. Post a link to your strop and we can take it from there.
Stitchawl