Beat the egg whites with an electric mixer until stiff. Line a baking sheet with parchment or waxed paper.
Put the sugar, corn syrup, and water in a medium-size heavy saucepan over medium-high heat. Stir to dissolve the sugar, bring to a boil and cook until the temperature reaches 260°F on a candy thermometer, or the hard-ball stage, when a bit of the mixture dropped into cold water holds its shape, 10 to 15 minutes.
Remove from the heat. Pour in a thin steady stream into the beaten egg whites and beat with an electric mixer on high for about 3 minutes, scraping down the sides of the bowl. Add the vanilla, and continue beating on high just until the candy starts to lose its gloss, 5 to 6 minutes.
When the beaters are lifted, the mixture should fall in a ribbon that mounds on itself. Add the pecans, stir to mix, and quickly drop the mixture by tablespoons onto the prepared sheet. If the mixture flattens out, beat again for 1 minute more. If the mixture is too thick to drop, beat in a few drops of hot water until the candy is a softer consistency.
Yield: about 24 pieces
If the candy is poured into a pan and cut into squares, you should have about 48 pieces.