1/3 cup sugar
2 tablespoons grated lime peel (green part only)
1/2 cup lime juice
4 1/2 cups diced (about 1/2 in.) honeydew melon
A little more sugar and lime juice to taste, if necessary
In a bowl, mash 1/3 cup sugar and lime peel with a spoon to release oils. Let stand 5 to 10 minutes. Stir 1/2 cup lime juice into sugar mixture. Pour mixture through a fine strainer into a blender or food processor; discard lime peel.
Add melon, a portion at a time, and whirl until smooth. Return puree to bowl. Taste, and if desired, add more sugar and lime juice. Nest bowl in ice and stir often until mixture is cold, 5 to 10 minutes.
Pour chilled puree into an ice cream maker (1-qt. or larger capacity). Freeze according to manufacturers directions or until sorbet is firm to scoop, dasher is hard to turn, or machine stops.