In medium saucepan, combine cranberries, sugar, allspice and water. Bring to a boil. Boil 10 minutes, stirring occasionally. Remove from heat; stir in raspberries. Cool 10 minutes.
Place half of mixture in food processor bowl with metal blade or blender container; process until smooth. Press pureed mixture through strainer into bowl to remove seeds; discard seeds. Repeat with remaining mixture.*
Pour into ungreased 8 or 9-inch pan. Cover with foil; freeze 2 hours, stirring occasionally. Without stirring, freeze an additional 2 hours or until firm.
To serve, let stand at room temperature for 15 to 20 minutes. Scoop into individual dessert dishes.