It’s a dilemma usually faced by classic rock artists, from U2 (who just played the TD Garden) to Joan Armatrading, in the midst of a five-night run at City Winery. How much do you play from your new album for an audience that doesn’t really know (or maybe even care about) versus the nostalgic songs that fans embrace?

Even artists who have risen over the last decade or two make the same decision – and they often lean toward their new stuff, as Ray LaMontagne and Neko Case did over the weekend on a double bill at Blue Hills Bank Pavilion.

“It’s not happening,” Ray LaMontagne responded to somebody in the crowd on Saturday, maybe to someone who requested an early acoustic favorite like the title track to his 2004 debut Trouble. The singer/songwriter completely ignored his first four Americana-styled albums, serving all nine tracks from his new Part of the Light and nothing that predated 2014’s psychedelic gateway Supernova (whose five-song sampling didn’t include its popular title track either).

At least LaMontagne, who’d switched to acoustic guitar before the fan exchange, earned a warm reception for yearning new love song “Such a Simple Thing.” His new album does bridge a gap between his old and new work, though the previous new songs he offered – “No Answer Arrives” (laced with spacey shards from My Morning Jacket guitarist Carl Broemel) and “As Black as Blood is Blue” – mined dark riff-rock more in line with LaMontagne’s last album Ouroboros. Broemel also blew sparks over extended jams that capped Pink Floyd-ish set-closer “Goodbye New Sky” and a snarling “Hey No Pressure,” the peak of an Ouroboros-heavy encore. By then, some fans had hit the exits. A great set, with psychedelic visuals on TV-like screens and LaMontagne chiming his electric guitar to match his rich, grainy voice. But maybe not for those who wanted their old troubadour.

Neko Case likewise played twice as much of her new album Hell-On in her opening set, and while her clarion voice helped lift “Oracles of the Maritimes” and “Winnie,” fans on Sunday responded most strongly to “This Tornado Loves You” and set-closer “Hold On, Hold On,” the sole entry from Fox Confessor Brings the Flood. That definitive 2006 album sealed Case’s place as a unique vocalist beyond alt-country or Americana labels, yet she rarely weaves songs structured with choruses that elicit mainstream appeal.

Another distinctive voice, British artist Joan Armatrading built a huge following in the ’70s and ’80s as an acoustic singer/songwriter and (increasingly) a rocker who reflected her Caribbean upbringing in her reggae-inflected palette. But she’s been largely off the map in recent years, and her five-night Boston stand that ends Thursday (part of an six-city tour of City Winery venues) offered the chance to see Armatrading in an intimate, mostly acoustic solo setting. She mostly played acoustic guitar, a few songs on piano, and the rarity “True Love” on electronic keyboard.

So, Armatrading also has a new album, Not Too Far Away, which she featured in its entirety across a 10-song first set at City Winery on Sunday. The album proved engaging in the pristine small-hall setting, from apt opener “I Like it When We’re Together” to the syncopated “Invisible (Blue Light”) and piano ballad “Always in My Dreams” (the exception was “Any Place,” with the trite lyric “As long as I’m with you, any place will do”). Armatrading’s distinctive voice, deep and in falsetto, was intact and if anyone in the full house was worried, she returned for a 12-song second frame that touched on both hits and deep cuts, including the briskly strummed “Mama Mercy.” A dinky keyboard patch under “Drop the Pilot” and a canned sax solo in encore “Love and Affection” seemed a little distracting, but for the most part, electronic enhancements to her vocals and guitar from her pedalboard provided minimal icing to an earthy return that proved tasteful and fulfilling.

When you better split the difference between the new and old, maybe you can have it both ways.