The outside of the nostril opening is called the alar margin or nostril base. There are a variety of unattractive features that can be improved upon in this area of the nose and some can be done under local anesthesia. It is usually a matter of "too wide" but with careful analysis one can find many different causes for this appearance.  If the nostril margin "flares out" too much, a section can be removed to improve this contour. If the nostril attaches to the cheek too far away from the midline, there are other techniques which address this problem. Sometimes the tip and bridge can have good shape and position, but the area where the nose meets the upper lip is sunken backwards into the face too far. This can be nicely improved with grafts or implants. Sometimes from trauma or previous older techniques in surgery the tip drops back and the nostril widen.  Correcting the tip problem here greatly improves the shape of the nostrils.  There are also newer grafting techniques that place very small pieces of cartilage buried along the nostril rim that shape the rim by their slight stiffness.