Place frozen banana pieces in a food processor. Pulse with on and off motions until finely chopped; whirl until pureed. Spoon puree into a bowl and place in the freezer.
Add berries to the food processor. Whirl until pureed. Remove bananas from the freezer. Swirl in berry puree. Serve at once. Makes 6 servings.
Approximate nutritional analysis: 83 calories per 1/2-cup serving; 1g protein; 21g carbohydrate; 4g fat (4% of calories); 2g fiber; 1.5mg sodium; 37% of the Daily Value for vitamin C; 22% for vitamin B6.