Cuban · Flor de Cana
Flor de Cana ages its white rum four years and then filters the colour back out, so there is real barrel behind a clear spirit. It is also made without added sugar, which is unusual and which shows immediately in a drink this simple.

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The one thing that matters
Because the rum is drier than most, you can push the syrup up slightly, to a full ounce, without the drink turning sweet.
A clean white rum with some character. Flor de Cana's four year old is aged and then filtered clear, so it brings barrel depth without colour. Bacardi Superior is the lighter, more traditional choice.
Not strictly, but white rum is the classic and it keeps the lime sharp. Aged rum makes a rounder drink that is closer to a rum sour than a daiquiri.