Bring the water to a boil in a large saucepan. Add the sugar and stir to dissolve. Add the berries and simmer, stirring occasionally, for 5-10 minutes, or until they begin to break down. Add extra sugar to taste as needed.
Stir the cornstarch into the 3 tablespoons of cold water, and then whisk the cornstarch slurry into the simmering berries to thicken it into a loose, pudding-like consistency. (Keep in mind, the berries will thicken even more as they cool. You might not need all of the slurry. Then again you might need more. It depends on the berries.).
Remove from heat and pour the berries into a large bowl or individual serving dishes. Cover with plastic wrap and chill well.
Serve topped with a little cream or with a dollop of whipped cream.