Why is a troupe called The Attic Ensemble Company playing on the first floor?

Shouldn’t Attic be performing in a room right under a theater’s roof?

But the first-rate off-off-Broadway company has for a while been ensconced on the first floor of The Flea Theatre on White Street.

Perhaps it’s called The Attic because it does such lofty productions. In years past, artistic director Laura Braza has staged a dynamic The Time of Your Life and a magnificent Strictly Dishonorable. Now she’s taken on John Patrick Shanley’s The Dreamer Examines His Pillow, his 1986 effort that served as his third professionally produced play.

It lasted 40 performances in the tiny 47th Street Theatre, which didn’t bode well for the playwright’s career. But Shanley would of course go on to win an Oscar for Moonstruck as well as a Tony and Pulitzer Prize for Doubt.

What Shanley wrote here, whether he intended to or not, is his Sam Shepard play. It’s most noticeably in the style of the 1983 Fool for Love, whose first stage direction is “The play is to be performed relentlessly.”

Braza has precisely staged The Dreamer Examines His Pillow in that forest-fire fashion. And while Shanley’s play doesn’t literally have its characters bouncing off the walls as Shepard’s brood does, it has plenty of confrontation among its three characters. One is very angry, one doesn’t want to get uninvolved and one is semi-clueless.

Donna bangs on the door of Tommy’s apartment. There’s no doubt from the look of it that this is not a doorman building, so we don’t take issue that she has access to it. Of course, we could rightfully assume that this is a tenement where you’d have to throw down a key from a window to let a visitor in the front door.

For a while, Donna and Tommy were lovers. But in recent months, he’s been seeing her sister Mona. Donna is furious and verbally lets him have it. Tommy, meanwhile, seems at times to be barely involved in the conversation. He keeps talking about his efforts to improve himself.

Anyone with those goals, however, wouldn’t be sleeping with a 16-year-old, which indeed Mona is. Needless to say, his violating the statutory rape law exacerbates Donna’s ire.

Wouldn’t you think that once Tommy admits to having had sex with the girl that Donna would call the cops? Instead she says she’s going to let her father know what happened and that he’ll come over and straighten Tommy out.

Saying “I’m gonna tell my father!” seems tantamount to a remark often heard in grammar school quarrels. Where adults are involved, it’s hardly the go-to solution. But this isn’t what strikes us as most incongruous.

Donna, you see, is still in love with Tommy.

Or so she says. This is at the very most a love-hate relationship. Anyone watching her yelling and screaming would judge her feelings far more in the hate camp than in a love nest.

Considering that Tommy has such a hard time concentrating on what Donna has to say, what with his drifting in and out of her rants, he hardly seems like much of a catch. That he’s been dealing drugs for a living isn’t anything to put on his resume, either.

So we can’t get behind them or their relationship. That makes us just wish they’d both go away.

So is the attraction physical? Perhaps, but when Tommy makes romantic overtures (and, oh, is that a euphemism), Donna rebuffs them. And yet she keeps proclaiming her love. Never mind going to get your father, Donna; go out and get another boyfriend.

But go to fetch her father Donna does – not that Dad, as he’s solely known, is happy to see her. Even as Donna is banging on the door, he’s moaning aloud to himself (Shanley’s too-easy way of handling exposition) that grown children only come to visit when they want something. Dad does have another good perception when he notes that Donna is the type of daughter remembers an off-hand remark he made 15 years ago and still holds it against him.

So do you think Dad will go visit Tommy? Shanley believes he would — and has the man show up in a tuxedo. That’s not the only incongruous costume we’ll see before this third and final scene ends. En route, the fate that Donna and Tommy experience isn’t one that you’d wish on them. You may well want to yell out “Don’t!” before the play’s final moments. That the conclusion is at least 99 and 44/100ths percent unbelievable doesn’t help, either.

That said, the entire 90-minute intermissionless enterprise is worth seeing for Lauren Nicole Cipoletti, who makes us believe that she has found this character, which may be more than any member of the audience can. She has a fervent devotion to the material as she rages, stomps and screams during the exhausting first scene, Although the script allows her to settle down a bit after that, she still experiences quite a workout. Cipoletti must be sleeping non-stop each night without benefit of Advil-PM.

Shane Patrick Kearns’s Tommy aptly captures the demeanor of someone who’s just been hit in the forehead with a two-by-four – or who’s been smoking or injecting a lot of his capital. Dennis Parlato’s Dad goes from disconnected to too connected, but it’s the script that’s at fault and not the fine actor.

The set for this enterprise posed a challenge for designer Julia Noulin-Mérat. We first see Tommy’s rat-trap replete with damaged walls, but that’s followed by a visit to Dad’s digs. Noulin-Mérat, undoubtedly working on a limited budget, did what she could to spruce up the single set for Scene Two with a few new pieces of furniture here and a new painting there. But those depressing walls remain and indicate a far less successful man than Dad has been.

And what does the title mean? Don’t ask, because it isn’t terribly well-answered. Just thank the Lord that John Patrick Shanley grew out of his Sam Shepard phase.