At the first visit, patients will undergo a complete clinical examination and body weight (BW), height (HT), blood pressure (SBP/DBP) and heart rate (HR) will be also measured. Body mass index (BMI) will be calculated as BW/HT2 and expressed in kg/m2. We consider overweight patients with BMI> 25 and < 30 whilst frankly obese are those with BMI > 30. Patients will be followed-up for two months when treatment for the prevention of headache (usually the calcium entry blocker flunarizine 5 mg/day) will be added to the habitual dietary regimen. At the end of this run-in period all patients will be randomly attributed to one of the following two dietary regimens: a low lipid diet with a lipid content < 20% of the total daily energy intake and a normal lipid diet with a lipid intake between 25-30% of the total daily energy intake. In both diet lipid intake is mostly represented by monounsaturated fatty acids (14% in the low lipid and 19% in the normal lipid diet) with a low intake of saturated fats (< 8%of the total calories, which is the percentage usually recommend in our diets). Patients will be followed-up for 2 months at the end of which they will be switched to the alternative dietary regimen.