Walk into any hardware store or specialist shop and you will find a wall of little crayon looking bars. Green. White. Black. Red. Each one promising finer edges, more refined polish, better results. Most of it is marketing. Some of it is real. Here is the honest version.
What a compound actually does
A stropping compound is abrasive particles suspended in a wax binder. When you rub it on leather or wood, the binder smears. The abrasive stays. When you draw the edge of a knife over that surface, the particles remove a tiny amount of steel. That is it. The whole story.
Everything else is grit size.
The three you need
Most people do not need more than two compounds. Many do not need any.
Green. Chromium oxide. Roughly half a micron. This is the workhorse. If you buy one compound, buy this one. It will take a knife that came off a fine stone and polish the edge enough to shave arm hair cleanly. For ninety five percent of kitchen and carry knives, green is the last step you need.
White. Aluminum oxide. Coarser than green, around three microns. Useful as a bridge step between a medium stone and a final polish. If you are restoring an edge and do not want to pull out a water stone, white on leather works.
Black. Silicon carbide. Coarser still. This is for scary sharp competition finishes and for people who enjoy the process. It does not make your kitchen knife cut tomatoes better.
A stropped edge is not a different edge. It is the same edge, cleaned up.
What compounds will not do
They will not rescue a dull knife. If your knife will not slice a sheet of paper with authority, stropping is not the answer. Go to a stone. Stropping is maintenance, not repair.
They will not make a bad knife into a good one. The steel is the steel. Compound on a cheap knife produces a sharp cheap knife. It does not produce a Sukenari.
The simple routine
One. Finish on a stone. Six thousand grit is plenty for most knives.
Two. Load a leather strop with green compound. Rub the bar on the leather, back and forth, firmly, until the surface looks uniformly shiny.
Three. Strop twenty strokes per side, light pressure, spine leading. Not edge leading. Edge leading will ruin the strop and round the edge.
Four. That is it.
Do this once a week on a carry knife. Twice a year for a kitchen knife that gets proper stone work. You will not need to touch a stone for months.
What I would skip
Anything sold as a kit with five colors and an instructional DVD. Anything with glitter in it, which I have actually seen. Anything that does not list the abrasive by name and particle size on the label. If a company will not tell you what is in the bar, they are selling you wax.
Keep it simple. Green on leather. A steady hand. A knife that will be sharp for a long, long time.