In 1983, British singer Elvis Costello, a longtime fan of Baker, hired the trumpeter to play a solo on his song “Shipbuilding”, from the album Punch the Clock. The song was a top 40 hit in the UK, and exposed Baker’s music to a new audience. Later, Baker often featured Costello’s song “Almost Blue” (inspired by Baker’s version of “The Thrill Is Gone”) in his live sets, and recorded the song on Let’s Get Lost, a documentary film about his life.