Giftedness and perfectionism go hand in hand, to such a degree that perfectionism is one of the diagnostic traits of gifted children. (The politically correct terms for prefectionism are now "persistent" and "intense".) Hoagies All Things Gifted page is a terrific place to start researching the subject of perfectionism in gifted kids.
What the experts seem to agree on is that there are two types of perfectionists: the ones who will work to the point of burn out to succeed and the ones who decide being perfect all the time is too hard, so why bother trying to do anything well? In my family, we have one of each. Chester has been struggling at school at least since second grade, when he wasn't finishing class assignments because his perfect handwriting was taking too long. #1 Son, on the other hand, is a not-quite-B-average-report-card-carrying classic underachiever. (Wolfie either isn't a perfectionist or he just hasn't hit the wall yet.)
For many years, I thought Chester was more high achiever than gifted (see this article for the differences. You'll need to scroll down some.) His test scores are now saying differently, which is terrific, but I'm almost afraid to tell him, for fear it will put even more stress on his already tightly-wound system. He's a much harder worker than his brothers, always has been. Still he struggles to get his assignments in, even though he appears to be on task 90% of the time. He's also very sensitive to anything that might be construed as criticism. His teachers are all saying there is a problem, but if he refuses to talk about it, how can we figure out what the problem is?