While some people say to lean the bike, what they are really doing is countersteering by pushing on the bars - on the same side as the direction of the turn - just the opposite of what you would do when turning at a very slow speed. Countersteering is what causes the bike to lean and turn sharper - not body English. Anyone who'e ridden a motorcyle very much knows that if you're turning right and going too wide, you push harder on the right side of the bars (countersteering) to lean the bike more and turn sharper. A bicycle works the same way, but with a road bike's hook shaped bars, the countersteering action isn't as obvious.

A common cause of newbie motorcycle wrecks is a failure to turn tight enough. Rather than pushing harder on the right side of the bars (to turn right), the rider panics, quits pushing and goes across the centerline into oncomng traffic. When I first started riding hairpin mountain descent on a bicycle, I had not taken a motorcycle training course. I was riding a Colnago that has a lot of steering trail. If you didn't apply constant pressure to the bars, the bike would straighten up quickly and not turn. After taking the motorcyle training, I have a lot better understanding of how a bike turns. I've ridden thousands of miles in the mountains and never had a problem.