Set inside a cramped New York apartment where adult sisters on the brink of estrangement await their father’s last breath, “His Three Daughters,” from writer-director Azazel Jacobs, is no farce. But within its measured, melancholic tempo, it boasts its fair share of bracing humor. As this claustrophobic indie — one of the year’s best — makes exquisitely clear, there’s no easy way to pre-grieve, especially when dysfunction is the dominant language.

There’s an acting master class to savor, as one might expect from a cast that includes Carrie Coon, Elizabeth Olsen and Natasha Lyonne, each of them in career-best form. Apart or together, they play to perfection an alternatingly discordant and touching piece about family fractures that in the hands of Jacobs, a veteran of discomfiting empathy (“Terri,” “The Lovers”), rarely hits a wrong note.

Coon is this chamber trio’s honking reed as oldest sib Katie, a restless, controlling mother with a problem teen (whom we never see, just hear about) and a bulldozer quality. In the grim circumstances of the failing health of their dad (a briefly glimpsed Jay O. Sanders), Katie keeps up a vinegary commentary of What Isn’t Right and What’s Always Annoying, but also Why It’s Not Her Fault yet will invariably be Her Cross to Bear.

Though naturally prickly, she’s on good enough terms with Christina (Olsen), also a married mom and the ensemble’s plaintive woodwind. Christina’s traveled the farthest (West coast), yet in her airy, apologetic, hippie-ish countenance — she’s got that motherhood-is-a-gift vibe — seems least connected to the reality of the swirling tensions. Nearly all of Katie’s negative energy is directed toward their stoner stepsister, Rachel (Lyonne, the wary violin), Dad’s adopted daughter from his second marriage.

Katie sees Rachel as little more than a useless layabout waiting to claim the apartment, even though Rachel had been the live-in caregiver before things turned. Rachel will bite back if cornered (and Lyonne’s raspy acidity is, as ever, a treat), but she’d rather hole up in her room, smoke away her grief and keep track of her sports bets than play dutiful sister/daughter — at least not in a way that feeds Katie’s judgmental bossiness or Christina’s diplomatic mindfulness.

In this vibrating, believable scenario, everyone is so relatably breakable while bearing their fragility in such unique ways — again, what a cast — that in one sense, all Jacobs needs do is let breathe what’s there. But we also sense that in this terrible finality, there’s a healing intimacy just around the corner, if only alignment can be found. Those glimmers of hope make for an appealing background hum.

Despite having only one interior location, “His Three Daughters” — deftly photographed by Sam Levy and edited by Jacobs) — never feels like a filmed play. We’re inside it, feeling the unresolvedness of the past and present within these modest, lived-in digs. The strange electricity of waiting is conveyed with every shot, whether it holds one, two or all three of its sterling leads in the frame.

Toward the end, when the time for rapprochement is near, Jacobs pulls his one surprise, making an unsuspectingly bold and semi-fanciful swerve, foreshadowed by a story Christina tells that reveals how their twice-widowed dad felt about death. It’s a twist for sure, and it feels like it shouldn’t work. But somehow — because it’s so wonderfully written — it does, landing with affection and grace within a depiction of a few floundering, turbulent days.