Cut the nectarines in half and remove the pits. Cut the fruit into 1-inch wedges and put them in a medium-size saucepan with ¼ cup water. Cook over medium heat for about 10 minutes, stirring occasionally, until the fruit softens and is just tender.

Working carefully with the hot mixture, purée the fruit in a blender or pass through a food mill. Strain the purée through a sieve. There should be about 1½ cups.

Stir ½ cup water and 1/3 to ½ cup sugar into the mixture (less sugar for white nectarines). If the mixture is still warm, the sugar will dissolve easily; if not, you may have to heat it gently, stirring until the sugar dissolves.

Taste the purée and, if needed, add a few drops of lemon juice or kirsch—or both. Refrigerate the nectarine purée and freeze according to the instructions for your ice cream machine.