Peel the potatoes. If they are new potatoes, there should be at least eight. Leave them whole. If they are large Idaho potatoes, quarter them, which is to say, cut each potato into four equal pieces.

Place the potatoes in a saucepan and add water to cover and salt to taste. Bring to the boil and simmer until tender, 15 or 20 minutes, depending on size. Do not overcook.

Drain and add the butter, shaking the saucepan until the pieces are coated.