Calexico and Iron & Wine were both fresh off of career-defining albums when they joined forces for the first time nearly 15 years ago. Tex-Mex band Calexico had recently found success with Feast of Wire (2003), while Iron & Wine's Sam Beam had just released the near-perfect Our Endless Numbered Days (2004) and Woman King EP (2005). A prominent spot on a generation-defining soundtrack for a little film called Garden State also helped Iron & Wine rise to new indie singer-songwriter heights.

With just seven songs and clocking in at under half an hour, Calexico and Iron & Wine's 2005 collaboration EP In the Reins was short and sweet, but entirely unforgettable. Given Beam's songwriting prowess and Calexico's expert level of instrumentation, the two were a musical match made in heaven. A decade and a half later, they have reunited for a new album, Years to Burn, as well as a lengthy tour.

Irish folk singer Lisa O'Neill opens up the show at Edinburgh's Usher Hall with beautiful, haunting songs about the Irishwoman who shot Mussolini ('Violet Gibson') and the Dublin docklands workers who lost their jobs to machines between the 1960s and 1980s ('Rock the Machine'). Those in the audience who are early enough to catch her set are noticeably entranced.

Sam Beam and Calexico frontman Joey Burns soon take centre stage, backed by other members of Calexico, opening with Years to Burn track 'Follow the Water' and new takes on old favourites 'He Lays in the Reins' and 'History of Lovers'. They tackle Calexico's 'Glimpse', which Beam says was the first Calexico song he ever heard. A twangy take on Echo & the Bunnymen's 'Bring on the Dancing Horses' is pleasant, but played dangerously early on in the set.

Calexico's Jacob Valenzuela (also known as the 'Miles Davis of Mariachi') shines on 'Flores y Tamales' and 'The Bitter Suite', a three-part song that is particularly moving. The jam 'Red Dust' suddenly loses its steam when an upright bass solo goes on far too long. The band leaves Burns and Beam to do a few solo acoustic numbers: Iron & Wine's gorgeous 'Naked As We Came', Calexico's 'Fortune Teller' and new number 'In Your Own Time'. Burns personally thanks some friends who are in the audience and Beam jokes, 'I don't have any friends … so, thanks for coming'.

Unfortunately a noticeable number of audience members begin to leave early, but those who stay for the encore are treated to 'Father Mountain', one of Years to Burn's most memorable tracks. Beam and Burns' voices still go perfectly together, but with lengthy jam sessions and new arrangements of old songs, they struggle to capture the quiet crowd throughout the night.

Calexico and Iron & Wine, Liverpool Philharmonic Hall, Tue 19 Nov; The Bridgewater Hall, Manchester, Wed 20 Nov; Warwick Arts Centre, Coventry, Thu 21 Nov; Royal Festival Hall, London, Sat 23 Nov; De La Warr Pavilion, Bexhill-on-Sea, Sun 24 Nov.