Technically, corners would require you to have more power, so you can get back up to the 80 mph you're supposed to maintain on a 30 degree incline while towing your yacht uphill.
Not that any of us out here own yachts...
The weirdest experience I've ever had in mountain crawling was being passed by an old Land Rover with government plates. It was one of those diesel jobs that made something like sixty horses on a good day, and it had on tires that looked like they came with the car when it rolled off the line thirty years ago. I was doing 70, while he was going 80-90. Round the corners, no less. That's probably the only time you'll ever see one of those babies going over 50 mph.