In 2004 Cojoba had its first tour to the U.S., playing in New York and Boston, where they were invited to play at La Rivolta, an anarcha-feminist festival. The following year, they were invited to La Rivolta again, and took the opportunity to play in New York, as well as in Baltimore.

In 2006, the band started recording its next CD, Más allá del cielo, and its songs for a split CD, in collaboration with Spanish band Angela Chaning. In October of the following year, Taína and Javier moved to New York City and finished recording both albums there, in their apartment. In June 2007, Juanpi and David join Taína and Javier in New York. They went on tour again, playing in New York, Boston, and at the CLITfest in Richmond, Virginia.