See if you can make sense of this: JetBlue won’t advance-book the last pet slot on its flights—because it has to leave the space open for people who don’t book in advance.

I’m still trying to wrap my head around the policy. Here’s how it works. JetBlue permits three pets to travel in-cabin on any one flight. We called today to put our pet on a return leg from Florida on New Year’s day, only to be told that two pets were booked on our flight, and the third pet slot could not be given to us on the phone.

Why? Because that third slot is for use by airport personnel only.

And what do airport personnel do with that slot? They use it to aid owners who show up with animals unannounced and unreserved.

As a result, even though I followed protocol, and called a week in advance to bring my pet on a flight with space available for pet travel, JetBlue won’t book the pet travel because they need to see if a less prepared customer shows up and circumvents the policy.

On one level, this makes some sense. If I forgot to book my dog for a trip home, I too would want to slip on the flight with him. But JetBlue has taken this to an absurd extreme: yes, there is room on the flight; yes, you could conceivably fly with the pet; but no, you can’t determine this in advance. However, if I show up unannounced with my dog on New Year’s Day, and I’m the first person to do so on the flight, bingo! I can take him.

I can understand reserving theater seats for walk-up sales, but we’re talking about the transport of a live animal, one who will be in Florida and needs to get home to New York with its owners. JetBlue needs to either permit the advance booking of my dog or stop advertising a three-pets-per-flight policy that is a misnomer at best.

The message from JetBlue to me is simple: don’t bother following protocol. Just show up and demand to get on the plane. Yeah, because that will be fun on New Year’s. Looks like my dog is staying home—and I’m flying American next time.

Update, January 2: After seven phone calls—more than one to JetBlue corporate headquarters—the pooch flew happily home. I still have yet to receive a decent policy explanation from anyone, though. And we will be thinking twice whenever booking JetBlue flights to Florida.