Scoop melon from rind; remove seeds and cut into cubes. Puree in blender or processor. Add rum. Pour into a 9x13 inch pan, and freeze until just firm.

Allow ice cream to soften slightly. Cut frozen melon puree into cubes and whip in electric mixer.

Beat ice cream into melon. Freeze in ice cube trays; or pack in a 7-cup mold or airtight container. Store in freezer.

TO SERVE:

Invert on serving platter to unmold. Cover with warm damp cloth. Shake to release, let stand to soften slightly. Makes 7 cups, 8-10 servings.

NOTE: To make dessert less icy, freeze, beat again until creamy, not melted. Do not mold. Serve at once.