1 1/2 cups fresh blackberries
1 1/2 cups fresh blueberries
1/3-1/2 cup sugar
3 tbsp cornstarch
1-2 tbsp cold water
3 tbsp lime juice
1/3 cup demerara rum
Into a medium pot over low heat, combine berries and sugar. Crush half of the berries with a wooden spoon, then stir until juices run and sugar dissolves.
In a small bowl, whisk together cornstarch with water and lime juice. Add to berries, increase heat to medium. Stir briskly until the cornstarch is cooked and juices have thickened somewhat.
Adjust for acidity and sweetness as desired. Stir in rum and cook a minute longer. Cool and serve.