Hark! ‘Tis the peal of baleful bells, for a new semester has befallen Nevermore Academy, and freshly minted celebrity Wednesday Addams (Jenna Ortega) is, naturally, having none of it. “I liked it better when I was feared and hated,” she monotones as a flock of awestruck fellow students scrabbles around her ankles, autograph books a-flap.

Alas, her newfound fame is inescapable. “You’re kind of a big deal now after the whole saving the school from the demon pilgrim thing”, “It girl” Bianca (Joy Sunday) explains, as much to the viewer as to Wednesday, who is perhaps too busy administering icily efficient death-stares to her swooning fanbase to fully appreciate the ramifications of last season’s finale. The demon pilgrim thing? Ah, yes. The demon pilgrim thing. This, you may recall, was the climactic first-series kerfuffle surrounding one Joseph Crackstone, a bloodthirsty 17th-century pilgrim resurrected by dastardly botany teacher/beastmaster Marilyn Thornhill (Christina Ricci). Having already manipulated barista/actual monster Tyler Galpin (Hunter Doohan) into killing a series of pupils, police and local therapists, Thornhill planned on using the reanimated Crackstone to help her snuff out everyone else. Anyway, thanks to Wednesday the evildoers are now either exploded (Crackstone) or banged up (Thornhill and Galpin) and Nevermore, finally, is safe. Let joy – or at least guarded relief – be unconfined.

And now? Peace descends and the second series of this most deliciously macabre of smash-hit murder-mystery/high-school comedy dramas – or at least the four episodes available prior to the second half of the series being launched in September – can proceed in orderly fashion. Or not, as the case may be, because – ruh-roh – here comes another baddie! Specifically, here comes the Kansas City Scalper, a serial-killing, doll-collecting professional dog groomer in a velour tracksuit played, with much oleaginous glee, by Haley Joel Osment (of The Sixth Sense fame). In a breakneck pre-title sequence, we learn that Wednesday has spent her summer vacation tracking down the Scalper, being tied up by the Scalper, turning the tables on the Scalper, relieving the Scalper of his scalp and, finally, delivering the Scalper to justice. The ultimate significance of all this is moot (certainly the incident is, at least in this first episode, not referred to again) although only a berk would bet against the scalpless sod popping up at a later date and putting everyone off their Weetos.

It is, all in all, a very Wednesday introduction to the new season of Wednesday. That is; a hugely elaborate and wildly entertaining thing that happens very quickly and at great budgetary expense only to be promptly buried under the demands of a more immediately pressing plot strand. Which is, in this instance, Wednesday’s mystery stalker. Having emerged at the end of the last series, he/she/it has decided that our peerlessly nihilistic heroine must pay for something or other and has begun to leave her a series of increasingly shouty cryptic notes demanding she DO SOMETHING or other ABOUT THIS. Who is this irate foe? And what, precisely, is the nature of his/her/its beef?

Further unusualness abounds. A local private investigator is pecked to death by a distinctly murderous murder of crows. Wednesday has horrifying visions of ditzy roommate Enid (Emma Myers)’s imminent demise.

Nevermore, meanwhile, has an enthusiastic new principal in the Ned Flanders-y form of Barry Dort (Steve Buscemi, complete with statement knitwear and a moustache that follows you around the room). Dort is a Bruce Springsteen fan and is Not To Be Trusted.

Also straddling the tantalising first-episode divide between “seems quite nice, actually” and “is almost certainly a shapeshifting necromancer” is wispy new music teacher Isadora Capri (Billie Piper, clearly having a blast).

Similar fun is to be had in the return of Catherine Zeta-Jones’s, woozy, pillowy Morticia Addams if not in Luis Guzmán’s lumpy, grinning Gomez, whose character, as ever, seems oddly unfinished, as if he’d abandoned rehearsals halfway through, having been distracted, perhaps, by a scotch egg.

Minor quibbles aside, the season opener is wonderfully skittish and dense with jokes and plot. Tim Burton’s brisk direction ensures any embryonic wibbles of seriousness or sentimentality are swiftly squished by a shot of a rotting corpse, say, or a scene in which a flotilla of CGI caterpillars assemble themselves, apropos nothing, into the legend “BUG OFF”.

In the middle of it all, meanwhile, is Ortega’s Wednesday, whose charisma could power a thousand hearses. Not that she’d appreciate our enthusiasm. “Do not put me on a pedestal,” she warns her besotted schoolmates during her guest of honour speech at the disastrous inaugural Nevermore gala. “The only place I will lead you is off a cliff.”

The sensible among us are already preparing our parachutes.

• Wednesday season two is on Netflix.