From 1992 to 1997 he was music director of the Houston Grand Opera, after making a sudden debut with the company with a run of Verdi's Rigoletto, starring Leo Nucci in January 1990.

Throughout the 1990s Šutej also often conducted many concerts with some of the biggest names in both classical and popular music, such as José Carreras, Plácido Domingo, Montserrat Caballé, Dionne Warwick, Natalie Cole, Charles Aznavour, Diana Ross, Sissel Kyrkjebø, Andrea Rost, Vyacheslav Polozov, Ramón Vargas, Maria Guleghina, Ruggero Raimondi, Leo Nucci and many others.

In August 2008 Šutej was diagnosed with myeloid leukemia and later underwent chemotherapy treatment and a bone marrow transplantation procedure at the Fred Hutchinson Cancer Research Center in Seattle.

A new donor was found and he underwent a ten-hour surgery at KBC Zagreb on 29 September,[3] but his body rejected the transplant again, and due to postoperative complications Šutej died on 2 December 2009 at 58 years of age.

La Juive for ORF with Neil Shicoff, DVD Corona di Pietra with Plácido Domingo, Andrea Chénier" with Fabio Armiliato and Daniela Dessi.