It's no secret that in 2010, Alexa Ray Joel had a nose job. The daughter of Billy Joel had the plastic surgery to smooth down the large bump that used to be on the bridge of her nose. It also refined the tip, giving her a more petite and feminine look. Even after the plastic surgery she still has a rather long nose, but it looks much better than it used to. We can see Alexa Ray Joel before and after the nose job in the picture below. It shows her in 2009 (prior to the nose job) and in 2010 (after it).
Look at how pronounced the bridge of Alexa Ray Joel's nose is before the nose job. You don't really see how big of a difference the plastic surgery made until you look at a side by side profile picture.
You can see that even the width of her nose is now a little thinner.