The Dimpho di Kopane company, currently performing their four show repertoire at St. John the Divine, bring much-needed juice to old chestnuts. Their bouncy retelling of the Mystery cycle and their succulent “Carmen” laughed in the face of drier, conventional performances. Director Mark Dornford-May and the impossibly flexible musical director Charles Hazlewood make show after show heat with the blood of their fantastic performers.

So it seems strange that their most recent creation should be carved out of ice. Literally. But, then, adapting a fairy tale has inherent pitfalls. Narrating the “road-trip” aspect of the hero’s quest gets a production into instant hot water. The sequences follow on one another with no dramatic build – there’s always another brambly wood to get through, or another reindeer to coax.

On the same wooden rake and set of metal scaffolding that served their other productions, the company stands in front of a set of wooden stepladders. They are dressed in T-shirts and jeans, with only the high recitative of Pauline Malefane piercing the everydayness. She tells us about Satan’s mirror, a surface that twists everything beautiful and good. Though it broke long ago, the Snow Queen has blown shards of it into young Kaya’s heart and eye, and he may be lost to his village forever.

Kaya (the beatific Andile Kosi), who has only just come of age, learns to fight off lions and receives his mark from the village Elders. These dances of community, with women praying for their men’s safe return, jump and shake with life. But all too soon, the Snow Queen lures Kaya away, and his wife Gida (Andiswa Kedama) must embark on her long voyage to find him. She clambers over glaciers, talks to helpful animals and rivers, and meets with inevitable success, but it’s hard to feel moved by her impassive journey.

The team at work here is excellent. Dan Watkins’ resourceful production design makes ice caves out of ladders and costume designer Jessica Dornford-May kits everyone in fake leather for the triumphant homecoming. But too much time elapses between group numbers, and Ms. Kedama has the sweetness but not the strength to carry the show. If someone young in your family is a big fan of Andersen, or you’ve seen the rest of Dimpho di Kopane’s offerings already, then skate over to “The Snow Queen.” Otherwise, it’s cold enough outside – you’re better off with one of their hotter prospects.

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Where the South African company’s “The Mysteries” works to enliven medieval text, the SITI Company tries to distill it. In their current production of the 15th-century “Death and the Ploughman,” Anne Bogart and her solemn band consistently choose to chill and formalize their chosen morality play. The result is virtuosic – the three company members onstage work in eerie concert – but far too slick to grab on to.

Written by Johannes von Saaz in 1400, the play proceeds in short “chapters.” Railing against the death of his wife (the playwright himself was recently bereaved), the angry ploughman damns Death himself. He dares the Reaper to appear with him before God – for surely his work is the stuff of evil and must be judged. In each short sequence, the man presents his case and the spirit refutes it, neither of them departing far from his central argument. The ploughman repeatedly pitches Man’s virtues, while Death maintains that every garden must be weeded.

When Michael West’s translation appeared at the Gate Theater in London, Death appeared in three different bodies – as an old man, a cad, and the ploughman’s innocent wife. Ms. Bogart puts the dandy (Stephen Webber, with a bowler and furled umbrella) and the Woman (Ellen Lauren) on stage simultaneously with the farmer (Will Bond), turning the action into a triangular power struggle. At first, Ms. Lauren seems to be the silent memory of his wife. But as she gradually takes over more and more of the argument, the struggle becomes increasingly unequal. The ploughman can rage against Death, but how can he can he rage against the beloved Dead?

Ms. Bogart’s staging has an unfortunate effect. The abstract movement refuses straightforward illumination, but it also eschews any emotional impact. With a debate going on, it’s dangerous to do something so hypnotic – I found myself losing Death’s thread while I pondered the meaning of his umbrella.

“The Snow Queen” will be performed again November 18 & 26 (1047 Amsterdam Avenue, at 112th Street, 212-662-2133).

“Death and the Ploughman” until December 12 (136 East 13th Street, between Third and Fourth Avenues, 212-677-4210).