Possible Clues:

• Jack in a rhyme
• Jackfish
• Jack who could consume no fat, in a nursery rhyme
• 'Set a . . . . . to catch a herring'
• One who doesn't chew the fat?
• Fish for chap on a fat-free diet
• Nursery rhyme weight watcher
• A very small fish in parts
• Protective cover's rolled up displaying fish
• Jack, the picky eater