From Epicurious, mostly. Makes 2 drinks.
1 c blueberries (mine were frozen)
1/4 c grapefruit juice (or juice of your choice)
2 T sugar
a pinch of thyme (optional)
1/3 c rum (or more...)
juice of 1/2 lemon
Combine blueberries, juice, sugar, and thyme in a saucepan. Cook for a few minutes until the blueberries are falling apart. Strain, then add rum and lemon juice. Cool a bit, then shake with ice.
I saved the blueberry pulp to eat later, it's good. You could skip straining if you like, just cook the berries down a bit more.