William Shakespeare knew his way around comedy. His skill at employing both external and internal obstacles to keep inevitable romances from igniting remains unmatched, and no matter how dark his plays got, there was always room for a few gags.

Just because he was a master at comedy, however, doesn’t mean his plays are funny, at least not to modern ears. Today’s audiences may be groundling-esque in their cultural preferences, but Shakespeare troupes are invariably reduced to wacky accents and groaningly obvious sight gags.

So when I describe the Propeller company’s glorious “Taming of the Shrew” as the funniest Shakespeare production I have ever seen, this may sound like scant praise. It’s not: Director Edward Hall and his protean all-male troupe — which is also performing an above-average “Twelfth Night” in repertory at the Brooklyn Academy of Music — turn this obstreperous work into a comic gold mine, introducing all sorts of wonderful extraneous bits (many of them stemming from Michael Pavelka’s riotous costumes) in addition to excavating richly humorous truths from the text itself.

Even rarer, though, is Mr. Hall’s willingness to juxtapose these laughs with an unusually brutal gloss on Petruchio’s violent subjugation of Katherine, the titular shrew, culminating in a finale that is as unsettling as it is well reasoned. And so a blissfully funny Shakespeare shifts with almost imperceptible stealth into a harshly effective psychodrama. This is almost impossible to pull off, and Propeller’s skill at doing it is nothing short of miraculous.

“Shrew,” one of Shakespeare’s earliest works, opens with a rickety setup in which a drunken tinker named Christopher Sly is fooled into thinking he’s a lord; the rest of the story is depicted as a play-within-aplay performed for his benefit. Many companies skip this framing device entirely or at least plow through it as quickly as possible. Not Propeller. Mr. Hall instead interpolates a few lines from a prior, similarly titled play believed to be written by Shakespeare, using Sly (Dugald Bruce-Lockhart) as a psychological entry-point to the author’s (literally) bruising battle of the sexes.

Through a canny story-theater device, Sly himself is transformed into the central role of Petruchio. This frees Mr. Hall to delve more deeply than usual into the play’s disquieting gender dynamics. This Petruchio is a figment of the imagination, an omnipotent male fantasy who crows to his pals about his wife’s “new-built virtue and obedience.”

Propeller executes its cross-gender casting without a trace of camp. Jon Trenchard is a coquettish delight as Bianca, the fickle younger sister who can’t get married until her father (Bob Barrett) finds Kate a husband, and Simon Scardifield’s Katherine is even better. The buff, spiky-haired Mr. Scardifield can certainly hold his own against any of Kate’s suitors (many modern dance companies would envy the virtuosic grapplings shown here).

But despite this physical confidence, and the seeming parity that comes with it, Mr. Hall daringly conveys Kate’s “taming” through relentless physical and emotional violence. Mr. Scardifield makes it clear early on that Kate’s wrath is aimed primarily toward her hated self-image; when Petruchio briefly resorts to kind words of her beauty and charm during their courtship, her wary but nonetheless eager willingness to be convinced is touching — and her subsequent despondency that much more devastating.

By the time she reaches her infamous Act V monologue of submission, she has been reduced to thumb-sucking infantilism. As she reminds her fellow brides of the labors their husbands undertake “whilst thou liest warm at home, secure and safe,” she sneaks a devastated glance at her father, who has essentially sold her off to a monster. It’s hard not to notice that this bride has not known an instance of warmth, security, or even safety since her wedding day.

Propeller’s acuity at developing this wintry tone is so sharp that any laughs in “Shrew” could be seen as unnecessary or even unwelcome. Happily, neither is the case. Mr. Hall does a masterful job of moving actors around the jewel-box set — actors pour out of an array of wheeled wardrobes, also designed by Mr. Pavelka, and through the audience. Even the smallest roles brim with comic invention, and with nearly every actor armed with musical instruments (the marvelously eclectic score is credited collectively to Propeller), the play hums along with an infectious vitality. Just establishing these broad poles of comedy and tragedy in one production is a feat; reconciling them is a thing of wonder.

Shakespeare consistently cast the same actors in women’s roles, but Propeller mixes it up for its persuasive but lesser “Twelfth Night.” Petruchio and a few of Bianca’s suitors are now wearing the gowns, while the superb Mr. Scardifield has donned an evening coat for a P.G. Wodehousian take on the foppish Andrew Aguecheek. Mr. Hall’s use of music once again plays a pivotal role; propeller hails from the same British theater as the director John Doyle (of Broadway’s recent “Sweeney Todd” and “Company” revivals), and their shared do-it-yourself aesthetic is particularly noticeable here. More, however, doesn’t necessarily mean better. Too much of Mr. Hall’s staging involves the overused device of having “spooky” masked actors play eerie chords in the background.

The comic supporting characters in “Twelfth” — Toby Belch (Jason Baughan), Maria (a droll Chris Myles), Andrew Aguecheek, and the like — get their share of laughs, but the getting is more effortful. And while Mr. Hall once again tips the balance toward the play’s cruelty near the end, lingering over the humiliation of the pompous Malvolio (Mr. Barrett), the disparity in style proves less comfortable.

The plot — its heroine, Viola (Tam Williams, touchingly vulnerable and quite effective), spends nearly the entire play in drag and proves catnip to men and women alike — would seem to lend itself particularly well to Propeller’s all-male casting. This time, though, the lyrical passages are always competent and often lovely but rarely transcendent. By the standards of most Shakespeare productions, “Twelfth Night” would register as a qualified success; measured against the company’s expert work on “Shrew,” however, the strain of blending Shakespeare’s lumps and his too-often elusive laughs is apparent.

The notion of same-sex Shakespeare made a big splash when Cheek by Jowl unveiled its superb “As You Like It” in 1991, also at BAM. That group’s artistic director, Declan Donnellan, said at the time that audiences should be able to see Shakespeare cast in this historically accurate way once in their life. Since then, though, any number of high-profile productions have repeatedly met with success doing just that. Is enough enough?

Ultimately, all-male casting (or, for that matter, all-female casting) is like any other directorial conceit: If it sheds light on the production, it’s a good idea. If it doesn’t, it’s a gimmick. With its furiously disciplined acting company and its remarkable insights — even when it is merely very good, as opposed to wonderful — Propeller can do more or less whatever it likes to Shakespeare.

“The Taming of the Shrew” and “Twelfth Night” in repertory until April 1 (651 Fulton St., Brooklyn, 718-636-4100).