Combine the sugar and water in a small saucepan. Heat over medium heat for 3–5 minutes, stirring just until the sugar dissolves; do not boil vigorously. Remove from the heat and cool.

Add the strawberries, peeled kiwis, lime juice, lime zest, cooled syrup, optional corn syrup, agave, or honey, and salt to a blender. Puree until completely smooth.

Taste the puree before chilling. It should taste slightly sweeter and more intensely flavored than the finished sorbet because freezing dulls sweetness; adjust with a little more lime juice or sugar if needed.

For especially smooth sorbet, pour the puree through a fine-mesh strainer to remove strawberry seeds and some kiwi seeds. Refrigerate the mixture for at least 30 minutes, preferably 1 hour, until thoroughly cold.

Churn the cold mixture in an ice-cream maker according to the manufacturer's instructions, usually for 20–25 minutes. Transfer the softly frozen sorbet to a shallow, freezer-safe container, cover, and freeze for 2–4 hours until firm.

Let the sorbet stand at room temperature for 5–10 minutes before scooping. Serve in chilled bowls or glasses with a little lime zest, sliced strawberry, or a thin lime wheel.