Three of indie rock’s most interesting, idiosyncratic, and celebrated songwriters visit New York this week in the form of Wisconsin’s Bon Iver and Montreal’s Wolf Parade. The two acts may sound nothing alike — Bon Iver’s gentle folk is a world removed from Wolf Parade’s charged energy — but they share an interest in traditional, almost old-fashioned songwriting, which helps them achieve the palpable emotional power found in their songs.

Bon Iver, the solo outfit for singer-songwriter Justin Vernon, is the more instantly arresting act of the pair, if only because of the engaging intimacy contained in his debut album, “For Emma, Forever Ago.” Mr. Vernon wrote and recorded the album during a few months’ hibernation in northwestern Wisconsin after the breakup of his previous band, DeYarmond Edison, and apart from the occasional supplementary percussion beat or textural keyboard wash, it’s just the singer, his acoustic guitar, and a microphone.

Mr. Vernon self-released the album in 2007, and the American independent label Jagjaguwar reissued it earlier this year. He’ll bring the powerfully hushed results to the Bowery Ballroom tonight, and to the Music Hall of Williamsburg tomorrow.

Nearly every one of the album’s 10 tracks feels like a heartbreak song, though Mr. Vernon’s lyrics don’t traffic in shopworn clichés. Instead, he favors oblique suggestion and opaque narratives, singing songs that feel like they could be the result of a therapy session. In “Skinny Love,” Mr. Vernon sings about what sounds like a tumultuous relationship in which volatility may be the main attraction, but he cloaks such outright meanings in more shadowy sentences such as “I tell my love to wreck it all / cut out all the ropes and let me fall” and “I’ll be holding all the tickets / and you’ll be owning all the fines.”

And “Skinny Love” is one of his more literal songs. Elsewhere, Mr. Vernon suggests a comparison between finding out a lover’s secret and a car crash (“Blindsided”), mulls love strife with an uncanny suspicion (“Creature Fear”) and, in “For Emma,” turns thumbnail modernist poetry — “For every life / Forgo the parable / Seek the light / My knees are cold” — into a relationship autopsy in miniature.

What grounds such ephemeral writing are Mr. Vernon’s simple melodies and his expressive voice. Bon Iver songs are rarely more than a few guitar chords strummed together. Mostly, the beautifully haunting mood permeating “For Emma, Forever Ago” is established with a lone voice.

A quavering instrument, Mr. Vernon’s voice can deliver the hushed falsetto that shows up in so much contemporary folk — from Jeffrey Lewis and Vetiver to Iron and Wine’s Sam Beam and Grizzly Bear’s Daniel Rossen — but Mr. Vernon doesn’t dwell in that familiarly sotto voce mode. Instead, his voice somehow grows gritty and fragile as the tempo and his volume increases — qualities that lend an otherworldly vulnerability to the songs. In fact, the finest moments to be found on “For Emma” — the title track, “Lump Sum,” and the mesmerizing “The Wolves (Act I and II)” — hew closer to 1920s gospel music than anything in contemporary folk, the songs capturing an uneasy feeling of the sacred.

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Wolf Parade also reaches back to an earlier time with its sophomore release, “At Mount Zoomer” (Sub Pop), an impressive feat of alchemy from main songwriters Dan Boeckner and Spencer Krug. Where Wolf Parade’s 2005 debut, “Apologies to Queen Mary,” was another restless, jittery, dynamically expressive album in the vein of fellow Canadians Arcade Fire and Broken Social Scene, “At Mount Zoomer” funnels the big, fantastic ideas of over-inflated 1970s progressive rock through a stripped-down, indie-rock sieve to yield a taut yet expansive album of hot- and cold-running emotions.

That study in contrasts is due entirely to the divergent songwriting styles of Messrs. Boeckner and Krug. Mr. Boeckner, who also plays in Handsome Furs, favors sprawling, ramshackle songs of darting guitars and drums with spaces for vocals to carve out the principal melody. Mr. Krug, who also plays in Frog Eyes, favors ornate, hook-filled melodies that move with the nimble, piano-driven personality of musical theater. The band, which will appear at Terminal 5 on Thursday and Friday, alternates songs by each songwriter over the first eight tracks of the new album.

That this tension between tracks enhances rather than dilutes the album is a sly feat of sequencing and lyric writing. Messrs. Boeckner and Krug take on some outlandish subjects — witness Mr. Boeckner’s speculative mapping of his thoughts in “Soldier’s Grin,” and Mr. Krug’s metaphorical desert wandering in “Call It a Ritual” — but the album is held together by a florid imaginative streak and a solid format of anxious indie rock. “At Mount Zoomer” feels as though it should be a double-LP concept narrative stuffed with 15-minute opuses about wizards and elves. Instead, it’s a pleasurably skittish album of three-to-six-minute mini epics, with only the album’s finale — the jointly written “Kissing the Beehive” — surpassing the 10-minute mark. “Beehive” marks the only time Messrs. Boeckner and Krug acknowledge they’re working in prog vein, but they do it with such vim and energy that it doesn’t feel like an indulgence. They alternate verses, finally threading the album’s two personalities into one song — an effect that lends “At Mount Zoomer” a poetic cohesion at long last. If this album is any evidence, Messrs. Boeckner and Krug are never going to complement each in the ways that classic pop songwriting teams have; but their clashing individual personalities make for one very complex person of a band.

Bon Iver performs tonight at the Bowery Ballroom (6 Delancey St., between Chrystie Street and the Bowery, 212-533-2111) and tomorrow at the Music Hall of Williamsburg (66 N. 6th St., between Wythe and Kent streets, 718-486-5400). Wolf Parade performs Thursday and Friday at Terminal 5 (610 W. 56th St., between Eleventh and Twelfth avenues, 212-582-6600).