Can you guess the composer?

Okay, let’s have a little fun.  Here is a tune that I know that you know.  Question is, who wrote it?  I have been giving people this test for years and only one person knew the answer without having to look it up.  There are lots of versions, but I like this one by Harry Connick, Jr.
If you  knew the answer without looking it up let me know – now be honest!  I will reveal the composer in my next post.
This is a really nifty song, structure and chord wise.  I learned it for guitar and was amazed at how many chord changes there are for such a seemingly simple song.