¾ cup sugar
1 cup water
2½ cups fresh tangerine, Clementine, or Satsuma juice (from 12 to 14 fruits)
6 tablespoons fresh lime juice, or as needed.
To make sugar syrup, whisk together the sugar and water in a small saucepan, place over medium heat, and bring to a boil. Boil for about 30 seconds, or until the sugar dissolves and the mixture is clear. Remove from the heat an let cool completely before using. (This syrup may be made days. Or even weeks, in advance and stored in a tightly covered jar in the refrigerator.)
In a bowl, stir together the sugar syrup, tangerine juice, and 6 tablespoons lime juice. Taste and add more lime juice if needed to create a strong sweet-tart balance. Strain through a fine-mesh sieve positioned over a bowl. Cover with plastic wrap and refrigerate for at least 24 hours to chill well and develop the flavor.
Freeze the mixture in an ice-cream maker according to the manufacture’s directions.