Thousands of discs were released this year, but only 20 could make the final cut. With the most scientific of instruments (headphones, and sometimes CD players) we whittled down this year’s releases, and for the past two Thursdays, we’ve delivered five of our faves. Let us know what we missed, and what you loved.

LCD Soundsystem, Sounds of Silver (DFA)

James Murphy is the patron saint of downtown cool, and anything he or his record label touches instantly becomes an indie treasure. What’s most extraordinary about his sophomore release is its accessibility — at its heart, this is a bubblegum pop record, and not the salty organic kind of gum you buy at the health food co-op, either. We’re talking Bubblicious here, people. Long renowned for long-playing dance-floor remixes and shoe-shopping house beats — his other record this year, 45:33, provides an excellent example of that — Murphy’s work on Sounds of Silver is discreet, short and frequently to the point. “North American Scum” is precisely the kind of song you want with you at the gym, a self-deprecating slice of upbeat funk with lyrics that’ll never make the Republicans happy: “New York’s the greatest if you get someone to pay the rent . . . and it’s the furthest you can live from the government.” Then there’s the new wavy “Someone Great” and “All My Friends,” a song so suffused with nostalgia and desire it sounds like it belongs in a John Hughes movie. It’s excellent, easy to listen to and innately underground, and it’s been a long time since those three elements intersected in a pop album. Yes, there’s a sense of unrequited longing here, but so much the better for Murphy if he keeps producing work like this.

M.I.A., Kala (INTERSCOPE)

For her second album, thinking-liberal’s pop star M.I.A. traded political sloganeering and an abundance of hooks for something much simpler: an album of bangers, bamboo and otherwise. Compared to her 2005 debut, Arular, Kala‘s beats are more propulsive, its messages are more opaque and its cultural mining is even stronger. The resulting album is all prowess and ire and recontextualized sound. It is, at heart, a hip-hop record, and because it’s so effective and singular and forward-thinking, it’s the heart of hip-hop in ’07, period. As always, M.I.A.’s speak-singy vocals turn charisma into a fine art. Her personality is so huge, she’d have Rihanna‘s career if the world were fair. But then, her whole point seems to lie in reminding us that it isn’t.

Band of Horses, Cease To Begin (SUB POP)

Let’s forgive them the fact that their songs are all about mood and aura, rather than “feelings” or the problems that bring those “feelings” about. And let’s forgive them the fact that the singer veers into Supertramp territory now and again. Let’s just bathe in the eerie pomp of the chiming guitars and the rhythm section’s splashy forward motion. Like U2 sleeping over at the Jayhawks’ house, these guys make melancholy anthems that love to reverberate everywhere before they slink home with the echoes dissipating in the distance. Maybe it’s their recent move to North Carolina, but for a grandiose outfit there sure are quite a few moments where twang takes over. Dream pop disc of the year.

Radiohead, In Rainbows (ATO RECORDS)

It was a David & Goliath tale, if David were a band of insanely talented mope rockers and Goliath was the desperately floundering record industry. In short, the band revolutionized the music industry in 42 minutes and 34 seconds, with 10 songs: The band would offer its newest effort, In Rainbows, and whatever folks felt fit to pay, well, that’s the price of the album. It would be considered an impressive move by a lesser band. That the band was one of the most popular, and simultaneously respected, outfits in music today only compounds the coup. But to concentrate solely on marketing techniques, the implications of morality and the free market economic discussions this generates would miss the point: the band has made a gorgeous album. From the glitchy snares and waltzing jazz guitar of “15 Steps” to the stark, maker-meeting “Videotape” that seems to take its percussion from a funeral march, the album shows a marked change in the four years its been since Hail to the Thief. Gone is the politically tinged rock invective, and the verse-chorus-verse songs. Radiohead has made an opus, difficult to splice into song, and utterly captivating throughout.

The Shins, Wincing the Night Away (SUB POP)

It’s amazing James Mercer can get a word out, let alone an album, without choking altogether. Following the release of Oh, Inverted World, indie director Zach Braff latched on to it, using the majority of the album as the soundtrack to his movie, and even having his protagonist Natalie Portman utter the phrase: “This band will change your life.” That the band went on to make two records improving on the home-recording-honed formulae James Mercer devised for their debut is a feat. With their melodic base well-established, the band appeared to move outward from that point; experimenting with sound (“Sea Legs,” with its plastic bags popping as percussion) as well as perspective (“Phantom Limb” tells the story of two teenage lesbians alienated at their school).