trying to find a lost story...

When I was very, very young fell in love with a poignant story I read about a fairy who envied humans. She folded her wings behind her under her clothes and stretched out her toes so that they touched the ground (fairies normally couldn't touch the earth). At long last she could appear to be a normal girl, albeit one who walked tippy-toe, but it allowed her to walk among and befriend human girls.

That is all I remember of the story. Does anybody know of it? What is its name? Who is its author?