Combine ingredients in a medium saucepan. Cover and cook over medium heat until berry juices are released, about 1-2 minutes. Stir to moisten all the berries, cover again, and cook 3 more minutes. Uncover and cook just until the mixture has come to a full rolling boil. Boil for 1 minute. Cool.
Adjust flavor with additional teaspoons of sugar and/or drops of lemon juice.
Serve as a compote-like sauce, or puree in a food processor (and strain, if desired) for a more uniform consistency. Sauce may be made and refrigerated in a covered container a week ahead, or frozen for 6 months or longer.