I'd say cut out all sugar and refined carbs. Once you've settled into low carb mode (this is the hardest part), the experience of hunger changes completely. Without swings in blood glucose, and with cellular adaptation towards fatty acid metabolism, the 'sick' sort of hunger that most people think of as hunger goes away. I find that I can arbitrarily fast for up to 18 hours with no discomfort whatsoever. That was never the case before I stopped eating sugar and grains.
Replace those calories with saturated and monounsaturated fats (i.e. heavy cream or half-and-half instead of milk, eggs fried in butter or bacon fat instead of vegetable oil, plenty of olive oil-based dressings, avocados), and you won't believe the difference.