“Why is there no breeze?” is the kind of question that Marlboro-voiced Jeff Tweedy has on his mind these days. He’s put painkillers and wordy abstract expressionism (plus smokes) behind him, writing chitchat lyrics that make for instant intimacy. At times, however, the closeness feels almost sappy. Nothing is more dangerous than verse about dish-washing.

But whenever the oatmeal-colored ambling gets dull (“I was walking,” Mr. Tweedy monologues, “like I said, by myself”), something dramatic happens: sinuous Deadhead electric guitars bubble up and a 60’s-era Hammond organ hums a cross-eyed chord, or a lap-steel guitar yowls and Mr. Tweedy long-jumps into a never-before-heard falsetto. Instead of moseying into the pit of Billy Joel dentist-office soft rock, these songs unfold into colossal lushness (“Either Way”) or barroom bravura (“Walken”) or honky-tonk happiness (“What Light”).

“What Light,” as rural and uplifting and psychedelic as the Band on their 1968 debut, waltzes from a tiny guitar strum into a full-band feel-good hoedown. “If you feeel like singing a song / And you want other people to sing along,” Mr. Tweedy drawls, “Just sing what you feeeel / Don’t let anyone say it’s wrong.”

(If you can’t get to a meadow, but you’re into this sort of thing, “What Light” should be heard in a hammock on drugs.)

Only the appropriately titled “Please Be Patient with Me” fails to transform or unfurl: It’s an old-time song played on an old-time acoustic guitar, supplanted only briefly by a rickety electric. But like the drunkard Texas songwriter Townes Van Zandt or dozy Elliott Smith, it’s a pleasure to listen to Mr. Tweedy’s lonely finger-picking.

After all, Wilco’s dustiest songs have always been their best: On their rubbery, drug-addled last record, A Ghost Is Born, there was the pretty “Muzzle of Bees,” about silent suns and sea breeze; one album earlier, Yankee Hotel Foxtrot’s post-apocalyptic ballad “Jesus, etc” eulogized burnt stars and last cigarettes.

That was mellifluous music from a pinched-nerved band: The harmonies quivered and the violas sniveled. And way back in the last century, Wilco’s smiley pop masterpiece Summerteeth had the viciously serene “Via Chicago,” which begins, “I dreamed about killing you again last night / And it felt alright to me.” Have there been such anvil-hearted love songs since Roy Orbison?

That album had some scary psychoses beneath its glitter and grins, whereas Sky Blue Sky is essentially tranquil. But who could blame Mr. Tweedy for growing out of his ink-stained country-poet denim? He looks just fine in avuncular cords.

These new songs are fire-lit and snug: They saunter along until the band goes softly wild. That’s when six-man Wilco sports the Grateful Dead’s buttery grandness—after all, there are more musicians here than ever, including a new guitar player (and a new multi-instrumentalist).

The album’s opener, “Either Way,” begins with a characteristically cozy electric guitar, and Mr. Tweedy sings: “Maybe the sun will shine today / The clouds will blow away.” Jolly drums and a pastoral organ come in, plus feathery 70’s-era Randy Newman strings. But the song would still be flat-chested if it weren’t for a monstrous minor chord that creeps in: This album has a knack for getting curvy in all the right places.

Nevertheless, it’s still Wilco’s most syrupy-smooth record. The second track, “You Are My Face,” begins with a schmaltzy harmony (in which “sunshine” rhymes with “goldmine fulltime”). Thankfully, it only takes 90 seconds before the syrup gets replaced by grit, when the freshly added guitarist Nels Cline gnashes away.

How could one musician sound so much like chrome and margarine and gin? He’s a self-taught jazz guitarist who quotes Sun Ra and Garcia Lorca.

After a sprinkle of muddy and almost sappy blues, the second half of “Walken” becomes an electric, wave-your-Zippo extravaganza, interrupted only by Mr. Tweedy’s poignantly high-voiced epiphanies about a special little lady: “The more I think about it,” he howls twice, “I’m sure it’s you!” The piano player pounds, the drummer thrashes, and two guitars giddily wail like Lowell George (the Southern-fried Little Feat guitarist who liked speedballs and used a Sears & Roebuck spark-plug socket wrench as a guitar slide).

But Wilco’s guitars are at their most velvety on the album’s sleepy-eyed title track, where a lap steel tears up in the backdrop while Mr. Tweedy mumbles gloomy haikus: “With a sky blue sky / This rotten time / Wouldn’t seem so bad to me now.”

A sunnier haiku opens “Shake It Off” (“Sunlight angles on / A wooden floor at dawn / A ceiling fan is on”), which would be hugely bothersome if the song didn’t get so thunderous and tipsy after only two verses. The crusty, start-stop, cymbal-smashing spank of the “Shake If Off” chorus makes up for its sissy opening poetry.

It’s been 12 years since the band’s flannel-shirted barroom debut, 1995’s A.M., and they’ve rarely been as boozy as that song’s second half. But Sky Blue Sky is also Wilco at their clearest, airiest and most tender: Grateful Dead, eat your Californian hearts out.