As a set of lyrics, “Give Me a Nail,” from Mermaid Avenue Vol. III, bets that if it can make you believe its smallest promises — “Give me a nail, and I’ll nail it . . . Give me a row, and I’ll hoe it” — you’ll believe its last line: “Give me a world, and I’ll win it.” Bragg and Wilco kick off with a rousing, bashing fanfare, and within seconds you just want to play the song’s game, making up your own lines even as you follow from “Give me a bugle, and I’ll toot it” to “Give me a gun, and I’ll shoot it.” It sounds like a throwaway track on the seventh Byrds album — the throwaway that brings you back to the record when you’ve gotten tired of the masterpieces. Why not give this little a ditty a Top 40 arrangement? Who knows, this might be a single!

You can imagine even the musicians forgetting that, on paper, this song is of a piece with the Guthrie agit-prop or self-righteous chest-pounding numbers they’ve also tried and failed to turn into convincing music, maybe even to believe themselves: such automatic screeds as “My 30,000” or “All You Fascists,” or “Union Prayer.” So often, in Guthrie’s this-machine-kills-fascists numbers, flights of craft and inspiration are dragged down by the freight they’re forced to carry: the weighed and measured details of saying the politically proper thing in the politically proper way. In the 1930s, along with Pete Seeger, Guthrie wrote pacifist songs protesting American intervention against Hitler when the Hitler-Stalin pact was in force and that was the Communist Party line; as soon as Hitler invaded the Soviet Union the line changed and Roosevelt and Churchill, previously butchers and liars, had to be turned into heroes almost on a plane with Stalin. That kind of sellout — selling yourself and your song to the cause that seemed to need them more than you did — always stayed with Guthrie; it was a demon that, song to song, he escaped, and never altogether expunged. But with “Give Me a Nail,” Bragg and Wilco found a nonsense song hiding inside a manifesto, a manifesto hiding inside a nonsense song. That means the song itself is not playing by the rules, so there’s no reason to follow them.

That sense of fun and distant romance — memories of days that are perhaps lived more fully in a song than they ever were in life; a reach backwards or forwards to dreams of a better world, whether that means perfect sex or perfect justice — is all over the best performances here: the coolest, deepest alchemical collaborations. That happens with the first song on the first Mermaid Avenue, “Walt Whitman’s Niece” — who, you have to imagine, really was down in Greenwich Village after the War along with everybody else, maybe a great-niece, or a great-great niece, just one more person singing “Cumberland Gap,” drinking out of the bottle, and falling into bed with whoever looked as ambitious as she felt. The song opens with Bragg taking on the tone of a man going back to a night too good to talk about, even to himself, and so not talking about it — or almost not: “Did I ever tell you about, no, I can’t talk about that, they’d kill me, you wouldn’t believe me anyway.” This becomes the structure of the song, which opens with a couple of sailors tripping over each other in search of booze and pussy — there being no more proper way to put it. “Walked up to a big old building / I won’t say which building,” Bragg sings happily. “Walked up the stairs / Not to say which stairs” — and just like that, with a crowd of smelly drunks shouting Bragg through the choruses, Guthrie’s lyric sheet turns into a seemingly fated tangle of “Gloria,” Last Exit to Brooklyn, and Beach Boys Party! as performed by the Marx Brothers. Characters come to life as Bragg or Tweedy take on their voices, or stand off to the side, describing them in wonder: the night clerk and the customers in the smoky film noir ambiance of “Hot Rod Hotel,” which presumably can be translated as Hot Sheet Hotel; the street preacher in “Feed of Man,” so caught up in the frenzy of speaking the word of God, the words that are pounding in his head, that the words collapse: “On God’s plan print. That you dead a man.” There is the gorgeous “When the Roses Bloom Again,” with Jay Bennett’s free-flowing organ shooting through the tune, making the words seem like an excuse for the melody, just signposts for its evocation of a faraway heartbreak, a misery and beauty that the singer, or the musicians, can’t quite remember: they know it’s there, they just aren’t sure what it is.

That same delicacy, that lightness, is the whole story in the finest work here — a little miracle of affection and sympathy, collaboration and respect, as if from both sides across generations and from either side of the grave. “Way Over Yonder in the Minor Key” has a soft spring in its step as it follows the cadence of “Froggy Went A-Courtin’,” all to tell the tale of how, once, a young man talked to a young woman — or a 16-year-old boy talked to a 14-year-old girl — into crawling into a hollow tree, promising that “There ain’t nobody that can sing like me.” Billy Bragg keeps the promise, his voice high and almost breaking; as he sings, the turn of every word calls up the adventures he’s already had, the great deeds he will accomplish in the future, and the satisfaction he’ll have when, at the end of his life, he looks back on it all and smiles at how, back in that hollow tree, he talked her into taking off her shirt. The melody is strung so gracefully that it convinces you that, even if the man talking grew up to rob widows and orphans, he has lived a blessed life.

Natalie Merchant, coming in behind Bragg, opens up the song, making it the woman’s as much as the man’s; Eliza Carthy’s fiddle, seemingly waiting in the melody long before it chooses to take up Guthrie’s words, makes the story being told seem as old as the stories told in the oldest folk songs.

That is how this music works at its best: Bragg and Jay Bennett, playing organ and bouzouki, hearing “Froggy Went A-Courtin’” right there in the steps of Guthrie’s verses, hearing that he’d left the old song in his, passing it on to them, if they could find it, if they could pick up the clues he left and solve the case.