Edward III has long ranked as one of the “Shakespeare apocrypha,” which means the scholars are still squabbling, four centuries later, about how much the guy from Stratford-upon-Avon had to do with its authorship—assuming it was a guy from Stratford-upon-Avon doing the authoring in the first place, but that’s another academic wrangle. So it represents a Bardic oddity, a clunky, cobbled-together knockoff with whole swaths of theme and plot that seem like half-baked versions of better-known stories, from the nationalist posturing of Henry V to the fatal mysticism of the Scottish Play. Maybe it was the glovemaker’s kid plagiarizing himself, or writing a rough draft for other, better plays; maybe some 17th-century Shakespeare nut paraphrased the best of the Bard and passed it off as his own stuff. Whatever: Surely, when your city’s staging a six-month festival devoted to exploring Shakespeare from every imaginable angle, canonical curiosity is reason enough to have a go at a show like that.

So it’s a bonus that this scholarly novelty turns out to center on a chewy bit of continental politics, that it boasts more than one bit of first-class poetry, and that it’s being staged thoughtfully, if not quite thrillingly, in Joe Banno’s satisfyingly political, mostly modern-dress production for the Washington Shakespeare Company. It’s clear enough, and funny enough, and tidy enough in concept to make up for the occasional hurried passage of verse, the handful of undercooked characterizations, the labored scene changes on that giant conference table of a set.

Yes, I said “conference table”: Banno and set designer David C. Ghatan center the action on a broad slab of boardroom furniture, around which French and English factions gather to negotiate, Security Councilnstyle, over things like Edward’s claim to the throne of King John. (The French, as you’ll have deduced, are having none of it: Edward traces his lineage on the female side, and we know from Henry V that Salic Law says girls don’t count.)

The diplomatic face-offs play out briskly enough, with statesmen and generals trading disingenuously honeyed insults and bald, blistering threats by turns, but soon enough the action moves to more intimate quarters—which, given the staging conceit, means a good deal of furniture-moving, up and down the stairs at the cardinal points of the set. So while there’s a certain frisson in the exchanges between the suddenly lovestruck Edward and the woman who’s not his wife, a good bit of the air goes out of the production while the minor characters are lugging the chairs about.

What, didn’t I mention that? On his way to teach the French a lesson, Edward (Bruce Alan Rauscher, playing a sort of Everyking) detours by Roxborough Castle, in the vicinity of which those reliably ornery Scots (shades of Henry IV) have been making trouble again. No sooner does he clap eyes on the lady of the manor, though, than he’s forgotten the war, not to mention his queen. Before you can say “He’s gotta have it,” the confident statesman of Act I has been transformed into a petulant royal who’s prepared to pull rank if that’s what it takes—never mind that the lady’s husband is one of his more valiant captains. (Whoops, suddenly we’re in the middle of Measure for Measure.)

Hang tight, though, because that detour is a mere dramaturgical red herring: Shakespeare, or whoever, turns out to be less interested in the psychodynamics of this lustily complicated situation than in the tidy flights of rhetoric the king and his wary love object deploy. (Which is one argument for the play’s not being actual Shakespeare: Our boy had an uncanny knack for doing both at once.) Banno and his cast do what they can to ratchet up the suspense: There’s superb work from both Karen Novack as the Countess of Salisbury and Joe Palka as her put-upon father—strong-armed by the king, who’s suddenly got no scruples at all, into engineering the conquest when the lady resists. Palka and Novack wring genuinely plangent moments out of this bit’s better speeches—and then the writer gets bored with the game, so Edward suddenly recalls that he’s got a bunch of uppity frogs to chastise.

After which it’s battle, conference table, battle, callous moment involving Edward the Black Prince—the king’s wet-behind-the-ears son, whom Edward leaves unrelieved in a tight spot, the better to allow the stripling to prove himself at arms—more battle, more conference table, and so on. It gets a little dull, even with the French nobles glumly discussing evil portents and John Geoffrion’s righteous Prince Charles flaring impressively when King John’s ill temper threatens to disgrace the Valois family name.

So it’s something of a relief when E. the B.P. (an entertainingly gung-ho Jason McCool) finally gets to trounce the sneering Frenchies — and even more of one when Callie Kimball’s nicely no-nonsense Queen Phillipa arrives from England with one of those vanquished Scots in tow. Banno (who is, yes, the City Paper’s opera critic) has helped Rauscher and Kimball discover a deliciously textured bit of wordless byplay that says worlds about their relationship, which clearly runs on equal parts affection and exasperation; it’s a delight to watch, and it adds a comfortably human layer to a scene that’s otherwise all pomp and circumstance.

If Banno reaches a little too far in the next and final moment—more human frailty is what the charitable might argue he’s after, but it reads like an effort to make that almost-forgotten detour with the Countess seem less like a dropped stitch—he’s still managed to make a not-inconsequential evening out of a cipher of a show. And in a town as Shakespeare-mad as this one, a rarity that plays this respectably is nothing to sneeze at—no matter who’s not the author.