Eggs - WTF does 'over' mean?

During my travels in America I found myself eating breakfast out quite regularly. Being a fan of the egg, but knowing how my idea of a good scrambled egg differs with that of the majority, I often went for a fried egg. I would be asked how I'd like it cooked, and it was at this stage that my ignorance of egg terminology was laid bare. I know how I like it cooked, and could probably draw a picture, but this isn't a convenient method, ever. So I would ask for 'medium', which would always be corrected - apparently the word 'over' is necessary also. So over medium it was, every time. Although the cookedness of the egg would differ in each establishment I ate in, one thing remained reliable: there was absolutely nothing medium about an over medium egg. I kept reminding myself to look up the different terms used to order a decent fried egg, and today finally got round to it. Apparently an over medium egg is "cooked on both sides; the yolk is of medium consistency and the egg white is thoroughly cooked." This was precisely the consisency I was after, and yet it would seem that I was getting an over easy egg each time. Urgh.

I could, of course, have bypassed this issue at the first hurdle by simply asking the server what the different names mean, but I didn't want to sound like an idiot. So instead, I just ate a lot of partially cooked eggs. How I've learned my lesson.