1/4 Cup Superfine or regular Granulated Sugar
1/4 Cup Water
1 ripe Honeydew Melon, peeled, seeded, cut into 1/2-inch pieces
2/3 Cup fresh Lime Juice
Popsicle Molds and Sticks
Dissolve sugar in water by stirring if using superfine or by heating in a small heavy saucepan if using regular granulated (then cool).
Blend half of melon and half of lime juice in a blender until smooth. Add syrup and remaining melon and lime juice and purée until smooth. Force purée through a fine-mesh sieve into a 2-quart glass measure or bowl, pressing on solids and then discarding them.
Pour mixture into molds and freeze until slushy, about 2 hours.
Insert sticks, then freeze popsicles until completely hardened, at least 6 hours.