How do I get rid of unwanted cities in the new Clock app?

The new iOS 6 clock app is basic but meets my needs. Except for the part that I don't need to know the time in Cupertino, New York, Paris, Beijing or Tokyo, and I can't for the life of me figure out how to delete them. I've clicked everything on the screen and can only add clocks, not remove them. I want to add other places around the world but I don't want to have to scroll across the clock faces to get to the ones I am interested in.

Help make me feel stupid by telling me how to get rid of the preset clocks I don't want.