Grace Jones / Laurie Anderson, Corn Exchange/ Queen's Hall, Edinburgh, ****

How late it was, how late, when she finally favoured us with her presence, descending down specially constructed stairs in an outrageously voluminous dress and a face-obscuring hat. But that's what divas do, and three hours after the doors opened, Grace Jones towers over Edinburgh's Corn Exchange stage to the doomy bass-line throb of "Nightclubbing", stretching out winged arms like some Amazonian avenging angel.

In many ways, Jones was the precursor to today's celeb pop kids; the model-turned-singer, her athlete's body and snarling reputation as important as the music. But this was something of a coup for the third Triptych festival. The bravely eclectic offshoot of Scotland's blockbusting "T in The Park" summer rockfest reunited Jones with Sly Dunbar and Robbie Shakespeare, her musical mentors and the seminal drum & bass rhythm section behind the sharp, mechanised reggae-funk of 23 years ago.

One excitable fan shouted, "She looks fabulous!". Well, she always did, and at 54 her cheekbones remain sharp wedges, her legs still soar, and her furious eyes flashed as she purred though her gay disco hit of 1978, "I Need A Man", like a designer Eartha Kitt. You still got a hint of the androgynous power and bisexual iconography that hit the billboards and turntables in 1980.

The songs were beautifully poised on Sly and Robbie's darting percussion, hard-edged guitar couplets and maximum bass. Jones finished in a black crinoline, which she hoisted up to wiggle her still-shapely bum to the cheering audience during the magnificent groove of "Pull Up To The Bumper". Add a massive singalonga "Warm Leatherette", and a touching climax as she tangoed with Sly to "Private Life", and we were handbagged into submission, and loved every minute of it.

On the other side of town, another Eighties icon, Laurie Anderson, now Mrs Lou Reed, unveiled her new show, Happiness, which is about just that, or rather, our desperate attempts to attain it. It is essentially an episodic narrative delivered in her conspiratorial, answer-phone voice. Anderson stands stock-still beside boxes of electronic tricks that nudge and shift swathes of ambient sound around the Queens Hall. It's Edinburgh's least comfortable venue, a cold converted church with hard wooden pews intact. This seemed to amuse her and, bathed in shifting patterns of light, she played it up, a preacher for our times.

I had forgotten how funny she can be in her observance of the American human species. Little changed from the elfin New York punk she was back in the "O Superman" Eighties, she connects ancient Egypt to the American Civil War – they used bandages from mummies – a Buddhist outward-bound course to the disappearance of Bin Laden and Saddam, and considers how the Twin Towers collapsed in TV's ghostly silence. She makes us laugh while exposing our fault lines.