Chill your sorbet container before running the ice cream maker so when you transfer the sorbet to the freezer, it won't start melting.
Currant sorbet: Use 1 1/2 pounds fresh red or black currants, stems removed (4 1/4 cups). Bring currants and 1/2 cup water to a boil. Reduce heat, cover, and simmer until berries are soft, about 5 minutes. Puree mixture (do not add 1/3 cup water), and strain as above. Proceed using 1 to 1 1/4 cups simple syrup for red currants and 1 1/2 cups simple syrup for black.
Strawberry sorbet: Use 1 1/4 pounds strawberries, hulled (4 to 5 cups). Puree, and strain as above. Add 1 tablespoon fresh lemon juice along with 1 cup simple syrup.