I used to swirl my wine counterclockwise, due to being right handed. But once I started swirling it clockwise, and I've discovered, it makes my red wine taste better. It gives an additional depth to the flavour and really brings out and defines any undercurrents. I suspect this is because the awkward motion (since I'm used to going the other way) better aerates the wine than going smoothly counterclockwise.
However, I've also started to decant my wine on tennisballs and other isolation devices. In this case, I find the stablization better maintains a constant surface, which makes the aeration process more consistent for this phase of drinking.
But what's really important, I find is air purification/conditioning. Yes, you can argue that the air in your room is just that last mile, and that the wine has been exposed to air in the bottle and at the vineyard. But it's that last mile that matters the most.
I've started experimenting with power cords for my refridgerator to keep my white wines chilled more consistently. Will report later on whether ferrite cores or more exp cords make a huge difference. I'm excited at the prospect.
Best,
-Jason
Postscript: Oh, I know guys in France who are willing to bottle air from various regions in case you want to decant your wine in more pure air. It's expensive to ship though.