Swizzle the ingredients in a highball glass filled with crushed ice until they foam. Garnish with the lime wheel.
Those long Jamaican swizzles are hard to come by, but there is a solution. Go to the housewares store and buy a wooden spoon with a hole in the bowl of the spoon and a long handle. Put it between the palms of your hand and swizzle away. For a flavor twist, try using flavored syrups like Simple Syrup with vanilla beans or orgeat.