I've always found this song tiresome, and now I realize that when people sing it, they make it sound like a dirge. Try singing it with a gentle smile, and try to sound like you're singing it to someone you love, whose very existence makes you happy.

In other words, don't replicate the deadpan Frank Sinatra version.

Long ago, I learned in choir that one doesn't have to sing a high note loudly. Practice singing high notes softly by pretending to let the note drop on the floor. This is a good thing to do with the word "star" in this song.
=========
Somebody wrote a book called "Why People Don't Sing," and pointed out the most people don't sing nowadays, but when they do, they sing popular songs and they imitate every variation, every nuance, of the pop star's version exactly. I have vowed not to do that.