Only grip with your knees if you actually have to. Otherwise, relax any muscle you don't need in this minute to control the bike. I tend to hold tension in my quads and still have to consciously relax while riding. Gripping too hard for too long starts to hurt. And definitely hurts the next day.
I'm less confident about right turns than lefts, too, especially 90 degree corners in town. They're tighter than lefts, for one thing. So I tend to take a couple extra rights when I get home, to practice. Go around the block before going home.
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