Interpretation is pretty much a foreign concept in rock music. Singer songwriters do their own tunes and rarely bother with anyone else’s. Indeed, the rock world employs a somewhat derogatory term – a “cover”- as a way of putting down the act of singing a song written by someone else.

This difference is as much musical as philosophical. Show music has traditionally provided jazzmen with fertile soil for improvisation because these songs are so rich melodically and harmonically. Where jazz requires source material with more advanced chord changes (sevenths, ninths, and higher), most rock compositions use very basic, static harmonies that offer fewer possibilities.

Lea DeLaria’s last album, “Play It Cool,” jazzed up 11 show tunes of relatively recent vintage. Her new release, “Double Standards” (Telarc 85509) also has her looking in an unusual place for material. This time she turns 180 degrees away from Broadway to dig out material from what the album’s press release identifies as a “diverse selection of rock classics.”

Ms. DeLaria herself has said that “we had three rules for selection: the cut had to be in the college or alternative rock category, it had to be familiar, and most importantly, it had to swing.” Regarding the first two criteria, I pretty much have to take her word; I had never heard any of these songs before. But some friends loaned me copies of the original versions, by Green Day, Patti Smith, Jane’s Addiction, U2, and the like. From this evidence I can conclude that her third criteria remains completely unfulfilled – none of the original recordings even remotely swing. But Ms. DeLaria and her musicians make them do just that.

In their original versions, these songs aren’t about inspiring soloists and new interpretations so much as they are about laying down a certain kind of dance beat with a very specific attitude. To make these songs work as jazz, you have to rework them from the ground up – and put so much work into rewriting them that you might as well be writing completely new songs.

For the most part, Ms. DeLaria and her musical director Gil Goldstein have retained only the attitude and the lyrics of the originals – and in some cases not even that. Blondie’s “Call Me” is typical. It’s a 1980s song about wanting to have it all at once without waiting or challenge. For three minutes, a hot blonde screams that she wants to do the mattress mambo with you – you don’t have to do anything, just call her. Ms. DeLaria and Mr. Goldstein completely rethink it, making it work like one of Peggy Lee’s songs of seduction.

The difference between these songs and the kind jazz singers usually do is that the chords actually go somewhere, and not only that, but the lyric does the same – there’s a narrative progression from point A to B. Since that’s nowhere to be found in the words to “Call Me” (“any time, any place, any where”), it’s up to Ms. DeLaria to create an aura of mystery with her voice, adopting a timbre that vaguely suggests Lee or Billie Holiday late in their lives. Mr. Goldstein sets the whole thing in a haunting minor.

It’s hard to predict how the composers of these songs will react – obviously Ms. DeLaria is making them sound better than anybody ever dreamed they could. At the same time, she is pointing out how much work it takes to make pop songs of the last 20 years sound even as good as the humblest grade-B traditional standards. But “Double Standards” is a worthy effort – Lea DeLaria and Gil Goldstein have proven that it can be done. If you spot me humming “Tattooed Love Boys” by the Pretenders, now you know why.

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The central event of guitarist-singer John Pizzarelli’s new album “Knowing You” (Telarc 83615) is also a jazz version of a rock hit, Brian Wilson’s “God Only Knows.”

Twenty years ago, I was ready to write Mr. Pizzarelli off for attempting slavish imitations of Nat King Cole without possessing anything like the late singer-pianist’s colossal vocal chops. But over the years he has tempered the Cole influence with that of Rosemary Clooney, a great jazz-pop icon he learned from directly.

Mr. Pizzarelli worked with Clooney at the end of her life (most impressively on her 2000 album “Brazil”), when she was running out of wind but could still put a song over like nobody’s business. She was a formidable model of how much could be done with limited vocal chops. The lessons of Cole and Clooney are particularly useful in Mr. John Pizzarelli’s reinterpretation of “God Only Knows.”

Cole Porter took the most rudimentary songs of the day and made them sound beautiful and meaningful. He did this by taking them at absolute face value, bereft of irony, and this is the way Mr. John Pizzarelli sings “God Only Knows.”

In fact, Mr. John Pizzarelli so wants to strip it of virtuousity that he doesn’t even play guitar here – it’s the only track on “Knowing You” on which he just sings. There are no bass or drums either, just pianist Larry Goldings and tenor saxophonist Harry Allen. Mr. Goldings’s accompaniment is a little too busy, too 1960s baroque-and-roll, but Mr. Allen’s Stan Getz-ian tone is just perfect.

Most of the rest of “Knowing You” is equally excellent, roughly in the mold of Cole’s 1956 classic “After Midnight.” He makes Broadway show tunes swing (Richard Maltby and David Shire’s “Coffee, Black”), and makes jazz compositions sound like show tunes (Dave Frishberg’s “Quality Time”). He even is joined by his wife, Jessica Molaskey, on the fine original title track, “Knowing You.”

But that’s nothing for a guy who can make the Beach Boys sound as good as Frank Loesser or Sammy Cahn.

The John Pizzarelli Trio will perform May 3 and 8 at Birdland (315 W. 44th Street, between Eighth and Ninth Avenues, 212-581-3080).