Koch won a bronze medal with the United States national baseball team at the 1996 Summer Olympics in Atlanta.

On December 7, 2001, the Blue Jays, now under new management, traded Koch to the Oakland Athletics for Eric Hinske and Justin Miller.

Koch, however, gave up a critical ninth-inning home run to Minnesota's A. J. Pierzynski in the deciding game of the A's first-round playoff series.

On December 3, 2002, he was once again traded, this time to the Chicago White Sox along with two minor leaguers for Keith Foulke, Mark Johnson, Joe Valentine and cash, but was unable to replicate the successes he had experienced with Toronto or Oakland.

Due to wild inconsistency on the mound, Jerry Manuel removed Koch from the role of closer, relegating him to middle relief.