This randomized controlled trial tests the hypothesis that a reduction in intake of dietary fat will reduce the incidence of breast cancer. Women with more than 50% of the breast occupied by dense tissue on a mammogram have been recruited and allocated by a random (ie chance) process, to an intervention or control group. The intervention group has been taught how to reduce their fat intake to a target of 15% of total calories, while the control group continued their usual consumption of fat. Both groups have then been followed for at least 7 years and the number who develop breast cancer in each group will be compared