Remember how much time we used to spend (waste?) trying to work out the exact difference between a drama and a comedy? Luckily that’s been long solved with the catchall term “dramedy,” which made it safe for a half-hour show to be disturbingly dark, painfully real but also brutally funny.

Yet it’s worth asking if we went far enough in stripping away outdated expectations of genre. Is a one-hour show always supposed to be burdened with the heavy tone of drama? Is a half-hour show required to be even remotely funny? Is a half-hour show starring “Saturday Night Live” alum Bill Hader — known far and wide for his highly committed approach to slapsticky characters — supposed to be more funny than it is dark?

And here’s another question: Why does HBO put so much effort into finding the perfect one-hour drama (the quest for that elusive “next ‘Sopranos’ ” or “next ‘Wire,’ ” which leads to cowboy robots and other existential crises) when, time after time, some of its most moving and effective dramatic work is contained within its half-hour dramedies? “High Maintenance,” “Insecure,” “Getting On,” “Enlightened,” “Veep” — I could go on.

But to make a possibly long review shorter, let me just declare how far over the moon I am about “Barry,” a funny, violent, gripping and masterfully melancholy half-hour show created by Hader and “Silicon Valley” producer Alec Berg, which premieres Sunday. Drama? Dramedy? Comedy? I was too emotionally invested in its eight-episode story arc to label it. From start to finish, it’s just one hell of a show.

Hader, whose serious acting skills were already known to a few moviegoers (“The Skeleton Twins,” anyone?), stars as Barry Berkman, a former Marine living in the Midwest, who has been roped into the hit man business by a callously entrepreneurial relative, Fuches (Stephen Root), who sends him out on jobs to kill people.

Barry, who probably suffers some post-traumatic stress from his combat time in Iraq, justifies these murders as doing the world a small favor by getting rid of despicable criminals. He’s highly skilled at the work and, for the most part, morally numb to it.

Fuches tries to cheer Barry up by giving him a midwinter assignment in sunny Los Angeles, where a Chechen crime lord named Goran Pazar (Glenn Fleshler) has discovered his wife’s ongoing affair with her trainer, a dude named Ryan (Tyler Jacob Moore). Barry reluctantly tracks his mark around L.A., eventually winding up in Ryan’s acting class, which is taught by a small-time actor and self-styled master thespian named Gene Cousineau (Henry Winkler). While observing the class, Barry is mistaken for a prospective student, and something about the theater speaks to him. Could this be the calling he seeks?

Yes, I know — a few of you are thinking of the recent series adaptation of Elmore Leonard’s “Get Shorty,” which premiered last year on Epix and is also about a hit man who goes to L.A. and catches the showbiz bug. Trust me, by the end of the first episode it won’t even matter.

Barry’s reluctance to kill Ryan becomes an issue for the Chechens, including Goran’s hapless assistant, a hipster-wannabe named Noho Hank (“Gotham’s” Anthony Carrigan), who takes matters into his own hands and makes a bigger mess of things, once a determined L.A. police detective (“NCIS’s” Paula Newsome) is assigned to investigate Ryan’s murder.

Rather than cut bait and run home, Fuches decides that he and Barry should remain in L.A. and ally with the Chechens in their larger scheme to forcibly take over the business interests of a rival Bolivian crime lord. Barry agrees, mainly so he can devote more time to Cousineau’s acting course, where he quickly falls for an ambitious actress, Sally (Sarah Goldberg).

“Barry” is rich in all things — crime, violence, Hollywood satire — and its story moves swiftly along with a nail-biting degree of tension, sort of a “Breaking Bad” with 15 items or less.

The show also features an impressive supporting cast, starting with Winkler’s deliciously vain but sweetly paternal performance as a guru who genuinely cares for his acolytes. The memorable characters extend all the way down to those who play the individual thugs and striving actors who now populate Barry’s world, a place where a Bolivian kingpin constantly quotes Don Miguel Ruiz’s “The Four Agreements” and an order from Goran (in Russian subtitles) goes as follows: “Cut him up into manageable pieces. No one likes lugging around 50 kilos of torso.”

At the crucial center of all this is Hader, who, as Barry, gives a performance that is more about bottled-up rage and restraint than goofball antics. A sadness runs through everything he says. Coming uncorked at his most desperate moment, the skilled assassin in Barry finds proper motivation as an amateur actor. None of it would be believable if Hader had not also taken a big leap to this other side of his considerable talent. Whether you think it’s a comedy or drama, it’s a sublime bit of acting.

Barry (30 minutes) premieres Sunday at 10:30 p.m. on HBO.