Women who consumed three fourths of a tablespoon of monounsaturated fat could cut their breast cancer risk in half, according to a Swedish study involving 60,000 women. [Archives of Internal Medicine Jan. 12, 1998]. Possibly, these oils may help to balance fats in the body, which affects estrogen levels, says Claghorn. Substitute monos for margarine, butter and other trans-fatty acids (most fats in processed foods) and saturated fat sources. And eat mono-rich avocados and almonds.