The Jayhawks, The Barbican, London

The Jayhawks are one the great unsung American bands of the 20 century. Gary Louris and Mark Olson, the chief songwriters and mainstays of this sensational country-rock act, are comparable to Squeeze luminaries Glenn Tilbrook and Chris Difford, only without the hits and acclaim.

Their most successful single, “Waiting for the Sun”, only charted at No 20 in the US in 1992, which is galling given that they’ve created immaculate three-minute pop gems such as “Blue”, “Two Hearts” and “I’d Run Away”, all from 1995’s brilliant “failure” Tomorrow the Green Grass . The three tracks are highlights tonight, but you can’t escape the feeling that The Jayhawks are not entirely comfortable here; there’s minimal audience engagement and they seem to finish dramatically early, even though they’ve delivered a generous 21-song set. They feel like a finer proposition on record than in the flesh, but, still, what an exquisite sound, a heady blend of optimism and melancholy, and very redolent of The Byrds.

Louris, in his louche black suit jacket, resembles Jonathan Franzen, while the more gregarious Olson, in his check-shirt and jeans, is more like Dennis Hopper. Together, the five-piece look like fearsome academics from Yale, rocking out. Formed in 1985, the Minnesota outfit have reunited their strongest line-up from the mid-1990s, with Marc Perlman on bass, Karen Grotberg on keyboards and Tim O’Reagan on drums. And the fiftysomethings wig out impressively on new track “Cinnamon Love”, from 2011’s pleasing comeback album Mockingbird Time , and with their support act Chuck Prophet on the gospel-infused “Up Above My Head”. But it’s Louris and Olson’s harmonies that still delight, especially Olson’s cracked vocals on their best new track, the lament “Tiny Arrows”. The Jayhawks have always been compelling on the passing of time and fractured relationships, “I’d Run Away” being the finest example: “So we had a little baby boy/ But we knew it wouldn’t last too long/ Kind of what I had in mind/ But what I had in mind was strong.”

Other highlights include Olson’s “Miss Williams’ Guitar”, on which he sings about his former wife with gusto, the rootsy “Tampa to Tulsa” and their “big” hit “Waiting for the Sun”, from 1992’s Hollywood Town Hall .

Parts of this experience felt a tad underwhelming, but then this is an awkward band with a thorny history – lots of upheaval, band changes – and an act that never seems to belong in any one moment of time. However, their gorgeous pop songs will endure and the world is a better place with The Jayhawks in it.