The Edinburgh Festival Fringe may have only just started, but its key theatre venue is already setting the benchmark in its Traverse 2 space, with at least two major shows in a programme of utterly serious work.

Deep Cut
Star rating ****
Architecting
Star rating ***
Finished With Engines
Star rating ***
Free Outgoing
Star rating ***
Nocturne
Star rating ****
All at Traverse 2
The Edinburgh Festival Fringe may have only just started, but its key theatre venue is already setting the benchmark in its Traverse 2 space, with at least two major shows in a programme of utterly serious work. The tone is set from the off by the Cardiff-based Sherman Cymru company with Philip Ralph's play Deep Cut, named after the army barracks where four young squaddies died unexplained deaths that were dismissed as suicides.

Ralph focuses on 18-year-old Cheryl James, the Llangollen-born private who died in 1995, but whose case only came to prominence a decade later, after a BBC documentary. Through the words of Cheryl's parents and her barrack-room mates, a portrait emerges of a young girl who had everything to live for at a time when Britpop soundtracked the optimism of her generation. That picture unravels through a litany of gobbledegook and obfuscation on the part of the military authorities. Verbatim theatre can easily fall prey to moralising or sentimentalism, but Mick Gordon's production honours the sensitive material with a firm but gracefully understated rebuttal of the army's findings. The cast, led by a magnificent Ciaran McIntyre as Cheryl's father Des, rise to the challenge.

Arriving on stage just as three soldiers are cleared of manslaughter following the death of a colleague after a session of "beasting" - the charming name for what seems to be nothing more than institutional bullying - the tragic thing about Deep Cut is that it had to be written at all.

It's interesting how the younger generation of American theatre companies - post-Wooster Group as much as post-9/11 - have begun to build bridges with home-grown mavericks similarly weaned on pop culture and postmodern politicisation. So it is with the return of New York's the TEAM (Theatre of the Emerging American Moment), who developed Architecting over the past year with the Glasgow-based writer/director Davey Anderson in conjunction with the National Theatre of Scotland's Workshop scheme.

The play's starting point is Gone with the Wind, author Margaret Mitchell's trashy deep-south bodice-ripper made iconic by the big-screen version. From there, it proceeds by way of a narrative collage involving architect Henry Adams, a PC Gone with the Wind remake featuring Martin Luther King's ancestors, the theme-park redesigning of post-flood New Orleans, a Badlands-style runaway love story and a Scarlett O'Hara pageant.

From its opening bar-room serenade, it's not easy to spot the joins between Anderson's contribution and the TEAM's three co-writers under the guidance of director Rachel Chavkin and her restless cast. As is the way with the TEAM, it's a mess of ideas thrown into an audacious theatrical heap. Architecting nevertheless morphs into a far-off blues for a nation that prefers to keep its heroes squeaky-clean. And when a modern-day builder of dreams ditches the proposed regeneration of swampland shacks in favour of something more holistic, she's actually attempting to get back to the garden and rebuild Utopia. Frankly, the TEAM do give a damn.

There's more anglo-American fun to be had in the Arches' revival of Finished with Engines, Alan McKendrick's yo-ho-ho two-hander, which casts two sailors adrift on a nuclear observation vessel in enemy waters. Over 10 scenelets, Megan and would-be writer Hemingway tear metaphysical chunks out of each other like some David Mamet double-act setting sail on an all-at-sea Waiting for Godot.

As played by Stephanie Viola and Drew Friedman - both core members of missing-in-action Fringe favourites the Riot Group - it's a pithily intelligent exercise, part M*A*S*H, part absurdist satire of life on the frontline. Like Hemingway says, it's all material.

Crossing borders in a similar fashion is Free Outgoing by the Indian writer Anupama Chandrasekhar, a work developed through an international residency at the Royal Court. Chandrasekhar highlights a culture clash in a country that's dangerously high-tech, even as it remains in thrall to the prissiest of traditions, dealing with dissenters in a contrarily volatile manner bordering on hysteria.

When single mum Malina discovers that her teenage daughter Deepa has not only been intimate with a boy in school but that the filmed evidence is being passed round like a trophy, she too becomes the focus of the public's gaze on her private world. Her 16-year-old son Sharan is affected, and there are far wider reverberations in the wider community. Indhu Rubasingham's production is a surprisingly conventional piece of old-fashioned TV realism offset by a sleight-of-hand finale.

Finally, Adam Rapp's play Nocturne, given a transfixing, heart-in-mouth solo performance by Peter McDonald in Matt Wilde's production for the Almeida, is a devastating and unmissable piece of life-and-death story-telling about a runaway boy's return after accidentally killing his sister and subsequently causing his father to hold a pistol to his mouth. Despite this grim synopsis, Chicago-born Rapp's play, first produced in a multiple-actor version eight years ago, isn't some white-trash melodrama but seems more like a post-Beat elegy for lives lost and a self eventually reborn.

Our hero is a teenage pianist turned reclusive writer who buries himself in books to the extent that he even builds himself a table made of paperbacks. Unable to connect with women following his familial estrangement, guilt turns to purging via a thinly veiled novelisation of his own life. When his dying father contacts him, their final night together embraces both reconciliation and a kind of letting go. With each scene of low-key poetics punctuated by piano music, the story moves from abstract flourishes and soul-destroying poundings to a gradual harmonic peace.

As a man haunted by his sister, McDonald, clad in slacker plaid shirt and jeans, gives a compelling performance of a text rich with experience and understanding of the process of loss, grief and healing. Along with Deep Cut, albeit in a radically different way, this is one of the most honestly human performances you're likely to witness for some time.