Combine fruit purées in a medium bowl. Heat water and sugar, stirring until sugar dissolves. Add to purées with lime or lemon juice to taste.
If you have popsicle molds, fill them, leaving some room at the top to allow for expansion, set the lids in place and insert the sticks through the holes.
If you don’t have popsicle molds, fill small cups or empty yogurt tubs about 3/4 full, stretch plastic or foil across the top and make a small slit to insert sticks.
Freeze until firmly set, 3 to 4 hours. To remove the pops, first remove the lids or wrap, then squeeze the sides of the molds, twisting them slightly, to dislodge the pop. If necessary, rinse the outside of the molds under hot water first.