For the Puree:

1. Combine the water and sugar in a medium saucepan and set over medium heat. Stirring frequently, bring the mixture to a simmer, and cook for a few minutes or until the sugar is completely dissolved. Add the fruit and remove the pan from the heat. Allow the mixture to cool to room temperature.
2. Pour the mixture into a blender and blend until completely smooth. Set a fine-mesh strainer over a bowl or container and pour the puree through the strainer into the bowl. Stir in the lime juice.
3. Cover and chill the syrup until you are ready to use it.

For Two Mojitos:

1. Divide the lime juice, mint leaves, and fruit between two tall glasses. Muddle with a muddler or handle of a wooden spoon until the fruit is mostly mashed and the mint is very fragrant. Alternatively, you can muddle everything in one large glass or shaker and then divide it between the two glasses (muddle once instead of twice).
2. Add ice to the glasses and then divide the rum and syrup between the two glasses. Stir to combine everything and then top off the glasses with club soda, additional mint leaves, and lime wedges. Serve immediately.