As far as I’m concerned, no one should be allowed to cover the Beatles. It’s impossible to improve on the original, so why even try?

But Tori Amos’s new rendition of “Happiness is a Warm Gun” can hardly be called a cover. It’s an exploration of and a meditation on the original, with references (in the form of sampled sound bites) to John Lennon’s death and to the debate over the Second Amendment.

So, excepting the most obvious musical similarities, Amos’s version is not at all the same song. She breaks Lennon’s work down into its basic elements — irony and disillusioned romanticism — then rebuilds the song as her own.

This process is characteristic of “Strange Little Girls,” an album comprising entirely covers of songs written by men. Unlike a standard cover album, however, “Strange Little Girls” shows Amos bringing her own unique songwriting sensibility to every track. As a result, chords change, lyrics shift around, and song structure proves malleable.

For instance, Neil Young’s earnest folk ballad “Heart of Gold” twists into a constricted wail of what that can only be described as riot grrl-trance. If you listen hard, you can make out the original melody hidden in the background vocals, but a plowing guitar line (supplied by Adrian Belew of King Crimson/Talking Heads/Nine Inch Nails fame) replaces earthy acoustic strums, and Matt Chamberlain’s heavy percussion dominates the mix.

Also featured on “Strange Little Girls” is Eminem’s controversial murder narrative “97 Bonnie and Clyde.” In the new version, Amos replaces hip hop beats with eerie strings and muted bossa nova percussion.

Surprisingly, it works. The disturbing and desperate nature of the poetry emerges more fully in Amos’s song than in the original. She increases the impact of each terrifying line by slowing the pace and greatly altering the inflection. It is a chilling re-interpretation of a song often dismissed as cheap, violent sensationalism.

Renditions of Tom Waits’s “Time,” Depeche Mode’s “Enjoy the Silence,” and Velvet Underground’s “New Age” all stick fairly close to the originals, but Amos doesn’t limit herself to well-known songwriters. The “Strange Little Girls” track listing also includes Slayer, 10cc, Boomtown Rats and Joe Jackson. Post-punk philosopher Lloyd Cole’s standout song “Rattlesnakes,” reinvigorated by Amos, could make a terrific single; it certainly outclasses Amos’s catchy but conventional rendering of the Stranglers’ “Strange Little Girl.” In fact, none of the tracks have the marketing potential of “Spark” or “Concertina” (singles from her last two LPs), but the album as a whole remains a complex and rewarding work.

A necessity for Tori-philes, “Strange Little Girls” is also a great buy for pop fans and deconstructionists alike.