Wash and pick over cranberries. Place in saucepan with water and sugar. Bring to a boil, then reduce heat, stir, and simmer for 10 minutes or until cranberries burst.
Slightly mash the cranberries with the back of a wooden spoon until all skins are broken. Add cinnamon, nutmeg, and allspice. Mix well.
Remove from heat, and mix in the blueberries. Stir, breaking up some of the blueberries, but don't over mash them. Sauce will thicken as it cools.
Transfer to a bowl and let cool slightly before covering with plastic wrap and refrigerating until chilled.