Following in the wake of Kanye West, Swizz Beatz, Timbaland, and RZA, who’ve each successively claimed days of the week for sharing tunes via Twitter — G.O.O.D. Fridays, Monster Mondays, Timbo Thursdays, and Wu Wednesdays, repsectively — Dave Stewart (Eurythmics) joins the free frenzy, taking Saturday for something that departs from hip-hop.

Stewart kicked off his Saturday Songs last week with a two-fer, “I Know Your Name” and “Why Can’t We Be Friends” (download both here). But with December now upon us, not only have the musical gifts coming from the writer/producer/musician turned positively Christmas-y, yesterday there were three. First up is “Xmas Is For Lovers,” recorded in 2009 with his wife Anoushka Fisz, plus Diamond Fingers and Lady Fingers on backing vocals. The video for “Xmas Is For Lovers” was filmed at the legendary Capitol Records Studios in Hollywood:

The second festive treat Stewart pulled from his stocking is “I Want You For Christmas,” which he describes as “a kinda sexy one.” There’s no visual accompaniment to the song yet, so he’s offering a signed copy of Cocktail Christmas, an album not otherwise available, to the Twitter follower that makes the best home video to match:

But wait, there’s more. He followed up those two with a tune he wrote in one take. “Rock Fabulous Christmas,” is a gentle-bopping tune for “everyone single, married, [or] divorced who have worked hard all year.”

Clearly Stewart has the holiday spirit in spades, as he also contributed a recording of “White Christmas” from his aforementioned unreleased album to The Sounds of Christmas, Vol. 2, an all-star effort that benefits Sweet Relief.

UPDATE: The song gifts keep coming as Stewart has released a fourth original song, “Christmas In L.A.” Eurythmics fan blog ethrill.net has collected links to all of these free downloads.