Have butter at room temperature, but not extremely soft, or it will make for a really wet icing. Unwrap the butter, cut it into tablespoon sized pieces, cover, and sit out for one hour before use, do not sit it out the day before.
Have a mixer bowl with no fat in it, and a whisk, clean them with vinegar and salt, if nessecary, then rinse and dry.
Put the egg whites into the mixer bowl with a pinch of cream of tartar, and about 1/4 teaspoon salt, stir once or twice, fit into the mixer with the whisk attachment in place and ready. Set aside.
Grease a 2-cup glass measure with soft shortening, or use an ample quantity of vegetable cooking spray, set aside, by the stove.
Put the sugar and water into a 4-6 cup saucepan with a lid, stirring very briefly with a spoon to ensure that the sugar has been absorbed by the water on the bottom of the pot. Turn the heat to medium, and cook until the mixture starts to simmer. Cover with a lid. Cook 1-2 minutes (2 at the most), uncover, insert a candy thermometer, and cook, without interruption, until the sugar mixture reaches 238 degrees f.
While the sugar mixture is cooking, and keeping a steady eye on it, beat the egg whites at high or medium high intensity until this is stiff. (The object is to have the sugar mixture ready, the same time that the whites are beaten, I know that other recipes do not typically specify this process, but some do, and it's the method I learned, and am used to).
Transfer the sugar syrup, all at once, to the greased measure.
Pour it into the mixer, with it running, little at the time, avoiding the beaters entirely, and the side of the bowl, but allowing it (the sugar) to run gently down one spot of the side of the bowl, is preferable to having it sling on the beaters. Do not add it to fast, if there is any left in the cup, after a minute, throw it away, do not scrape it into the sauce.
Beat the mixture for 10 minutes moderately, or until the base is room temperature. Stir in the vanilla.
Beat in the butter, 1-2 tablespoons at the time.
Carefully transfer to a bowl, and chill to spreading consistency if nessecary. Add a few spoonfuls of rum before chilling, if required.