Critics of The Fiery Furnaces say the siblings’ quirky, indie-pop lacks structure and that it is just selfish indulgence made intentionally challenging and purposefully alienating.

Yet supporters swear by the band’s confusing genius and bizarre structures that make the expansive, abstractly thematic catalogue.

One thing both sides agree on — the band is prolific, four LPs and a B-sides collection since 2003. And until recently, it’s all been nearly perfect.

Before last year’s absurd “Rehearsing My Choir” — the album featuring the duo’s grandmother on lead vocals — Matt and Eleanor Friedberger’s atmospheric concept records had always been difficult to process, but the complex structures were so gorgeously arranged they were irresistible.

But not anymore.

Recorded more than a year ago — a month after “Choir” — the band’s most recent output is free of the conceptual restraints of its predecessor, but it still lacks the endearing oddities of earlier works.

The Friedberger’s experiments have reached a climax and come across as weird for the sake of weird. Instead of being content with layers of harpsichords fused on top of horns, synthesizers, bells, loops and every instrument under the Fiery sun, Eleanor’s jazzy vocals are now dubbed and re-dubbed atop each other — in reverse.

That’s right, backwards.

The only thing the duo should do backwards is travel, to a time before they lost that last shred of pop sensibility.

Even the band’s signature structures — brief mini-songs linked together with stop-on-a-dime changes and pieced into longer tracks — has begun to show its flaws.

Before, the approach was novel, as if Matt Friedberger’s sporadic world was too hectic, too cluttered to be restrained to four minutes of the same sound. Now, however, it appears he’s just unable to write real songs, and the days of 10-minute, multi-part epics were just a way to hide his inability to keep focused for more than a few measures.

Still, his music is the highlight of “Bitter Tea.” When stumbled upon, his pockets of organized musicianship — “Borneo,” “Police Sweater Blood Vow” and “Wanting You To Know” — rival his best songwriting.

It’s a good thing he’s able to still orchestrate these brief occasions of hope, as his lyrics may actually be the lowlight of the album. As his focus has become on more extensive musicianship, he has all but forgotten the necessity of words. Often, his sister is left repeating the same phrase — forwards and backwards — for long durations.

When not confined by indie egomania, the band can be brilliant. The Fiery Furnaces poses the ability to toe the line between justifiable experimentation and embraceable pop.

Yet, recently, the duo seems more concerned with staying credible through estrangement. And that is the most “Bitter” thing of all.