1. Pack 3 tablespoons ice cream into each of six 3-ounce disposable paper cups. Insert ice-pop sticks and freeze until firm, 1 hour. In a blender, combine peaches, sugar, and juice and puree until smooth, scraping down sides if necessary. Pour 1 tablespoon puree into each of six 6-ounce paper cups and freeze until firm, 1 hour. Reserve remaining puree.

2. Peel away paper from 3-ounce cups and place each ice cream pop into a larger cup of frozen puree. Pour enough reserved puree into cups to just cover ice cream. Freeze until solid, 4 hours (or up to 1 week). Unmold ice pops just before serving.