As the Woody Allen BFI season continues this month, it seems apt to start this second look back at the director’s back catalogue with the letter B: Bananas, Broadway Danny Rose and Bullets Over Broadway.

Bananas (1971)

Regarded as “one of his early, funny ones”, Bananas begins with a crowd stampeding a government office after El Presidente is assassinated. Amid the hordes of protestors, an American news reporter fights his way through the crowd with a wired microphone in hand.

It’s a chaotic opening scene and that confusion never lets up over a haphazard 80 minutes, but Bananas establishes a plot structure that Allen has returned to over the years: an unwitting, neurotic male chases after a female, only to get involved with a bunch of shady individuals – in this case, a group of rebels in the fictional dictatorship of San Marcos.

Farce quickly ensues, with harpists playing in cupboards, people wearing fake beards and men trying to buy porn magazines undetected in newsagents. It’s dated and very hit-and-miss, but like Marvin Hamlisch’s lively music, punctuated by bullet holes, the relentless slapstick of Bananas has an energy that’s hard to resist. Particularly in a hilarious one-man self-cross-examination in court, acted out by Allen with a frantic relish.

For everyone else, there's fun to be had when an uncredited Sylvester Stallone turns up as a thug on New York's public transport – yes, long before Rocky and The Expendables, Sly spent his early days beating up Jews on subway trains.

Broadway Danny Rose (1984)

13 years on from Bananas and Woody returned to his Bs with Broadway Danny Rose. And what a joy it is. The innocent schmuck here is Danny Rose, a perfectly-named showbiz agent for a range of talents that ITV would lap up: a blind xylophone player, a bird who plays the piano, an ice skating penguin (dressed as a rabbi) and, of course, a one-armed juggler.

Danny, trying to get lounge crooner Lou’s comeback going, finds himself tied up with Lou's latest fling, Tina. Literally, at one point. Blonde wigged, big breasted and with a brassy voice to match, she’s a classic Woody character played by an unrecognizable Mia Farrow.

Tina, naturally, is involved with the mob, an association that prompts a madcap dash from a bullet-ridden warehouse back to Broadway in time for Lou’s big show. Allen spends the film bumbling his way through great one-liners, but what really impresses is that they are driven by surprisingly developed characters - it's only two minutes longer than Bananas, but you can see that Allen's writing is now using the time far more efficiently.

Danny’s naïve loyalty to his acts, all of whom end up leaving him, is genuinely endearing. After a desperate hospital visit towards the end, rain starts to fall, looking like faded glitter on the gorgeous black-and-white screen (hats off to cinematographer Gordon Willis). It’s that unexpected depth (both visually and emotionally) that makes Broadway Danny Rose so charming.

The tale is presented using one of the director's favourite devices: a tabletop discussion between friends (all stand-up comedians). “I thought this was a funny story”, complains a listener. “What do you want me to do?” replies the narrator. “It’s not my life.”

Bullets Over Broadway (1994)

Bullets Over Broadway was my first Woody Allen film. As a result, I’ve always had a huge soft spot for it, but while people looking back at the 1990s usually skip ahead to the noughties, when Woody's wheels started to fall off, this 1994 comedy joins the list of underrated, overlooked pieces that prove the helmer still had it.

Returning to the world of showbiz (something Allen would also tackle with Celebrity and others), this time round the unsuspecting loser is the superb John Cusack as playwright David Shayne. Faced with financing troubles, Shayne is forced to cast a mafia floozy in his lead female role to secure funds. Unsurprisingly, she sucks.

Screeching her way through the silly script, Jennifer Tilly rivals Mia Farrow's earlier loud blonde in a cast that includes everyone from Rob Reiner to a moustached Jim Broadbent. Soon enough, philosophical mobster Chazz Palminteri (The Usual Suspects) is re-writing David’s play, while he’s off swooning over seasoned star Helen Sinclair (Dianne Wiest). "Don't speak!" she shushes as David tries to protest his devotion. It's hysterically hammy stuff.

At a typically brief 94 minutes, the whole thing zips along with a pace missing from most modern comedies, before climaxing in a smart, subversive sequence that easily rivals the rain-soaked romance of Andie MacDowell’s Four Weddings finale. “Do you love me as the artist or as the man?” demands an earnest Cusack, as a private proposal turns into an overwrought public debate about mechanics and Karl Marx.

Earlier, David passionately shouts: “It’s the duty of the theatre not to entertain, but to transform souls!” Carrying his familiar premise across three decades, Bullets Over Broadway may not manage the latter, but it sure as hell achieves the first part.

For more on Woody at the BFI, read our Hannah and Her Sisters review and our review of Zelig. To book tickets, visit the official BFI site.