Help me find this record/band

We are lucky enough to have a good alternative FM station that plays lots of good music. But if you're not alert you can miss the credits.

The song I'm looking for is most likely well known. I think it had Mick Jagger contributing on vocals. The lyrics of the refrain go something like this:

"She's making it all alright this time"

I know that is not much to go on but I'd like to hear that again.