In a small pot over medium heat, heat the water up to almost boiling.
Add the sugar and stir to dissolve.
Store homemade simple syrup in the refrigerator.
In a mixing glass, pour the juice from the lime over the mint. Muddle the mint but don’t overdo it. Place the squeezed lime parts into a serving (drinking) glass.
In a measuring glass, add the club soda. Pour the rum and simple syrup on top. Pour the mix into the mixing glass and stir all the ingredients together. Next, pour the contents of the mixing glass into the serving glass.
Top off the serving glass with ice, and garnish with a sprig or two of mint. Before placing the mint into the glass, slap it between your hands to release the mint oils.