Combine the wine, vinegar, and shallots in a saucepan. Reduce heavily, that is, more than three-fourths, but not au sec.
Incorporate the butter by one of two methods:
A. Set the pan over high heat. Add the butter all at once and beat vigorously with a wire whip. When the butter is about three-fourths melted, remove from the heat and continue to whip until the sauce is smooth. B. Set the pan over low heat. Add the butter a few pieces at a time, whipping constantly. When each addition is nearly melted, add a few more pieces. Continue until all the butter is added.
Pass the sauce through a fine strainer.
Hold the sauce in a warm, not hot, place until served. Stir or whip it from time to time.