The columella can be cut and sutured
This is a fairly simple procedure that can be done in the office. Any general plastic or facial plastic surgeon could do this. Your tip will still relax downward after the procedure. You also won't address any other areas of the nose with this move. Remember, what you can do with your hand and what is done after surgery has healed are not always the same thing. If you can find a good surgeon who agrees with your plan then you would have a good chance of it working. It would also be relatively easy to reduce the nostril size at the same time if still needed.
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Tip rhinoplasty versus full rhinoplasty
A tip rhinoplasty can only be performed for a select few individuals when the tip is out of balance with the remainder of the nose. Performing a tip rhinoplasty when there's a dorsal hump and overly projecting tip in a wide bridge will only lead to nose that is unbalanced and out of proportion. It is very important to have the nasal cartilages and bony components balance with each other and the entire nose must balance with your facial features