Between the Devil and the Deep Blue Sea, BAC, London

They glide, they soar, they loop the loop – in a charming display of Twenties-style eccentric dance, Jo-jo Pickering and Aila Floyd combine two enthusiasms of the decade, the charleston and aviation. Wearing fringed flapper skirts with aviator helmets and scarves, they're a joyously comic duo who would have cheered up any vaudeville house in that period. The girls, however, are the opening act for an entertainment that is much more complicated, both technically and emotionally.

With Between the Devil..., BAC again brings us, thank God, a Christmas show that has nothing to do with Christmas. The theme of the 1927 company's entertainment – innocence gone wrong – even runs counter to the holiday's stickier manifestations. In their sketches, two little girls do something worrying to their grandmother, a friend, and her cat; gingerbread men run amok; and Brownies get badges in illusion-shattering ("There is no Santa Claus, the tooth fairy has no face").

The performers – white-faced ladies in slinky black dresses – are Esme Appleton, Lillian Henley (who also provides silent-movie-style piano accompaniment), and Suzanne Andrade (writer and director). Within a proscenium by Mark Copeland that turns the stage into a giant toy theatre, and with the help of films and animations by Paul Barritt, they enact tales of dainty perversity. Little Helga, defying the warning sign ("Sin ahead! Do not be tempted!"), enters a forest clearing "bathed in bruise-blue light" and is never seen again. Two ladies turn topiary into a competitive sport that drives one to near-homicidal mania. Grandmother's advice ("The devil's boots don't creak!" and "Look into a mirror long enough, and a monkey will look back at you") turns out to be all too true.

In their drollery and childlike but sophisticated visual style, the playlets summon a multitude of echoes: Saul Steinberg, Edward Gorey, the deceptively demure little girls of the American folk artist Henry Darger, German children's books such as Max and Moritz and Struwwelpeter, the paper-cut animated films of Lotte Reiniger, and others. The show could be punchier, with more skits like the ones about topiary rage and an Edith Piaf-like cat for whom nine lives are one too few, and the tone at times veers perilously close to preciosity. But, at only 80 minutes, Between the Devil..., makes an amusing bonne bouche of an evening, a welcome sip of absinthe in the eggnog.

To 3 January (020-7223 2223)

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