In a five gallon bucket I mixed hot water with about a quarter cup of TSP and used a car wash brush to wash/mop the deck thoroughly. This is a serious cleaning solution but super stealth. No scrubbing bubbles, no mountain fresh scent. I did see a brown wake of muddy water stream from the trailing edge of the brush when I scrubbed back and forth.
I'll tell you something else, not captured in a picture. I was walking around the deck to take some of these pictures and I walked through the wet areas... Well, I slipped, cartoon style, feet and head at the same altitude, legs making a oval blur--blam! That spot was slicker than wet ice. After that I walked like a penguin.
Here are a couple before/after shots.
The observant reader will recall my expressions of fondness for the beauty of this wood. I imagine the exasperated replies "If you like it so much, why don't you marry it?" Whoops, I meant to say "Take a picture, it lasts longer." And so I have. It doesn't look like this anymore.