It is known that a large proportion of patients with arterial hypertension are undertreated. This may result in an increase of the incidence of cardiovascular events. On the other hand, aggressive reduction of blood pressure may increase cardiovascular events (J-curve phenomenon) in certain populations. This phenomenon may be seen in patients with coronary artery disease and left ventricular hypertrophy when the diastolic blood pressure decreases below 70-80 mm Hg, and the systolic blood pressure decreases below 130 mm Hg. This phenomenon is not seen in patients with stroke or renal disease. Thus, a safer and more conservative strategy should be applied in patients with coronary artery disease, left ventricular hypertrophy, elderly, and in patients with isolated systolic hypertension. This is depicted in the recently published European Society of Hypertension/European Society of Cardiology guidelines in which higher targets of blood pressure are suggested in certain cardiovascular diseases and in the elderly.