1. In a medium nonreactive saucepan, combine the cranberries and 0.75 cup water. Bring to a boil over moderate heat and boil, stirring occasionally, until the cranberries burst and the mixture reduces to 1- quarter cups, about dozen minutes. Remove from the heat and stir in one third cup of the sugar until dissolved. Strain the mixture through a coarse sieve and let the puree cool completely.

2. Preheat the oven to 275 degrees. Butter and flour a 9-by-2- 2 cm springform pan. In a large bowl, using an electric mixer, beat the cream cheese with the remaining 1 cup plus 2 tablespoons sugar and the vanilla at low speed until smooth. Beat in the eggs one at a time, beating until just blended. Stir in the sour cream.

3. Spoon half of the cream cheese mixture into the prepared pan. Drop 8 or 9 rounded teaspoons of the cranberry puree randomly over the top. Spoon half of the remaining cheesecake mixture evenly over the first layer and dot with half of the remaining puree. Repeat with the remaining cheesecake mixture and puree. (Avoid dropping puree in the center of more than 1 layer.) With a blunt knife, cut through the batter in a swirling motion to distribute the cranberry puree.

4. Place the pan on a baking sheet and bake in the lower part of the oven for 1 hour. Turn the oven off and leave the cheesecake in for 1 hour longer. Transfer the cake to a rack and let cook to room temperature. Cover and refrigerate overnight before serving.