Zavala grew up in Madrid listening to both the pre-WWII songs his grandparents used to play and the music his Peruvian father brought back from his travels to Latin America and Africa, as well the rock from the 70s and 80s that was popular in Spain. He credits these various influences for helping to shape his own style of guitar playing, one that pulled from blues, folk, flamenco, Afrobeat, Latin, and rock.

Though he enjoyed working with other artists, he was always writing his own music, as well. Some of the songs that ended up on his solo debut, titled DePedro, have their origins in the beginning of the decade. One of them, "Don't Leave Me Now"originally written for and performed by Amparanoia, was heard by the Arizona band Calexico. They added it to their live set list, and got in touch, asking Zavala to play it with them when they were touring Spain. In 2004 he joined them as a full-time touring guitarist, and when Jairo was getting ready to begin his new album, the band invited him to their studio in Tucson to record. In late 2007, Jairo left for Arizona with the melody and guitar parts for what would become DePedro in hand, purposefully leaving space for the other musicians to fill and shape.