TONIGHT'S MUST-SEE

"Billboard Music Awards," 7 p.m., Fox. Here's a two-hour burst from Las Vegas, honoring leaders in record sales and downloads and such. Also, Tony Bennett gets a career award. Mostly this offers lots of music. Performers include Janet Jackson, Ludacris, Gwen Stefani, Fergie, Mary J. Blige and The Fray.

"The Closer," 6 p.m., TNT. This week, TNT starts rerunning the second season of this terrific show at 8 p.m. Tuesdays. First, it has this fresh, two-hour story. Brenda (Kyra Sedgwick) gets a call from her old CIA mentor (William Daniels): A would-be defector was killed in Los Angeles; could she probe this on her own? That leads to a tangle of murdered agents and missing plutonium. It's a complex case, the second half of it directed by Sedgwick's husband, actor Kevin Bacon.

OF NOTE

"Rudolph's Shiny New Year" (7 p.m.), "The Year Without Santa Claus" (8 p.m.) and "Rudolph the Red-Nosed Reindeer and the Island of Misfit Toys" (9 p.m.), ABC Family. It's an all-animation night of "25 Days of Christmas." Two of these are obscure, but "Year Without a Santa Claus" has been popular. Next Monday, NBC airs a live-action, movie version.

"Desire" and "Fashion House," 7 and 8 p.m., MyNetwork (KFVE). These telenovelas lead into their finales Tuesday. Then two new ones start Wednesday, giving us fresh batches of beautiful and deeply troubled people to worry about.

"How I Met Your Mother," 7 p.m., CBS. A night of CBS reruns starts with Ted and Robin deeply in love, while Marshall mopes over his break-up with Lily. There are some funny moments, including a fantasy scene involving Lily and funk star George Clinton.

"The Class," 7:30 p.m., CBS. Nicole frets about the new friendship between her husband and Duncan — her old high school boyfriend, with whom she recently had a one-night stand.

"Heroes," 8 p.m., NBC. On one hand, characters deal with the Texas calamity: A killer, apparently seeking Claire, strangled a different cheerleader. Peter was charged with the murder. Meanwhile, there's a future tragedy to worry about; they learn more about the nuclear blast Isaac predicted.

"Supernanny" season-opener, 8 p.m., ABC. Tonight, we visit a home in which the three kids simply refuse to do obey their mom. She knows no solution except hitting — which is what she says her own parents did. It all works out, but only after an ugly, depressing hour.

"Studio 60 on the Sunset Strip," 9 p.m., NBC. As a Christmas show is created, Matt tries to bring some holiday spirit to his life.