In 1999 Yedid released his first CD, Compositions for Solo Piano, for the Musa label. This led to an invitation to perform in Scandinavia as the guest of the pianist Michael Smith, and to a joint recital in Sweden with the pianist Roland Pontinen. In 2001, Yedid’s second recording, Inner Outcry, was released, also for Musa. Yedid was commissioned to compose the suite Tachanun for the opening of “The Third Stream” festival in Vienna, Austria, in 2002. This composition has been performed many times in Israel including at the Kfar Blum Chamber Music Festival.
Myth of the Cave was commissioned by German record label Between the Lines. It was released in 2002. The five-movement piece has been performed at festivals in Germany and Austria, at the Vancouver International Jazz Festival in Canada and at the Tel Aviv Jazz Festival in Israel. It is based on Plato's allegory of the cave, about cave dwellers imprisoned in near-darkness since birth whose sense of reality is distorted. One of them escapes to the outside world, reports on what he has seen and is put to death for his revelations.
In 2003 Yedid composed Passions and Prayers - Sextet in homage to Jerusalem for Between the Lines. It is a technically complex and conceptually melancholy composition that premiered at the 2004 Israel Festival. The CD released in August 2005.
Reflections upon Six Images was commissioned for the Third Stream Festival in Vienna Austria in 2004. The music depicts the union and division of images, colors, textures, styles and cultures inspired by the world of the imagination. The composition was performed at the Vienna festival in September 2004 and at the Etnakhta concert series in November 2004 in Israel. The CD was released at the end of 2005.
In 2005, Yedid composed the Oud Bass Piano Trio, performed at the Sibiu, Festival in Romania, as well as in Australia, Canada, and the U.S. in May and September 2005. In 2002, he joined Israeli jazz saxophonist Abatte Barihun to form the duo Ras Deshen. They recorded their maiden album on September 2002, which featured a blend of Ethiopian music and Free improvisation jazz.