Nuts from trees, such as walnuts and almonds, can be an excellent source of the heart-healthy lipids that are provided by the good fats in tree nuts. It is strongly recommended that you do not add salt to these nuts. On the other hand, Pistachios are the nut variety that people with hypertension would benefit from eating the most. They appear to have the most effect on lowering your top and bottom blood pressure readings, which is highly advantageous. That is because they reduce your overall blood pressure.