Rudolph the red-nosed mystery...

A couple of years ago, I decided to whip up a mix CD of Christmas covers from a variety of sources. I found it today... without liner notes. I've been able to reconstruct the complete playlist and which disc it came from, but there's one song that's being elusive: the version of Rudolph the Red-Nosed Reindeer that I included. It sounds a lot like The Smithereens' version, but with more of a Brian Setzer twist.

Anyways, this is the list as I've reconstructed it. I've hyperlinked the Rudolph song in case someone can help source it.

1. Blue Christmas - Bruce Springsteen & Friends
2. Run Run Rudolph - Bryan Adams
3. Rock 'n' Roll Christmas - George Thorogood & The Destroyers
4. I Saw Mommy Kissing Santa Claus - John Cougar Mellencamp
5. All Alone On Christmas - Darlene Love
6. What Christmas Means To Me - Stevie Wonder
7. Winter Wonderland - Eurythmics
8. Silent Night - The Primitives
9. White Christmas - Doug and The Slugs
10. I Want an Alien for X-Mas - Fountains of Wayne
11. Here Comes Santa Claus - Clockhammers
12. Jingle Bells - Jumpin' Jimmy and The Mistletones
13. Christmas Song - Dave Matthews & Tim Reynolds
14. Christmastime Has Come - Smashing Pumpkins
15. Christmas Song (Chestnuts Roasting on an Open Fire) - Hoodoo Gurus
16. The First Noel - Crash Test Dummies
17. Please Come Home For Christmas - Pet Benatar
18. Merry Christmas Baby - Sheryl Crow & Eric Clapton
19. Rudolph the Red-Nosed Reindeer - (?)
20. Rockin' Around the Christmas Tree - Ronnie Spector & Darlene Love
21. Frosty The Snowman - Leon Redbone & Dr. John
22. Carolina Christmas - Squirrel Nut Zippers
23. Christmas (Baby Please Come Home) - U2
24. Christmas All Over Again - Tom Petty
25. Have Yourself a Merry Little Christmas - Pretenders