White Sox carried two left-handed relievers into the start of the 2000 season: Eyre and Kelly Wunsch. After going 1–1 with a 6.63 ERA in a few scattered outings, Eyre was optioned to Charlotte on May 26, with fellow left-hander Jesús Peña called up to take his place. Eyre suspected that the reason for the demotion had less to do with his own performance and more with the overcrowded bullpen, telling reporters, "When you only pitch four innings in a month, something's got to be wrong." He fractured his left hand in Charlotte on August 31 after being struck by a line drive off the bat of a member of the Norfolk Tides, but recorded the out by throwing the ball to first base with his uninjured right hand. Eyre made 47 appearances for Charlotte, all in relief, and went 3–2 with a 3.00 ERA, 12 saves, and 46 strikeouts in 48 innings. Toronto Blue Jays (2001–2002) On November 8, 2000, the White Sox traded Eyre to the Toronto Blue Jays in exchange for pitching prospect Gary Glover. His new teammates began to notice Eyre's constant fidgeting on the mound during the 2001 season, and the team therapist suggested that he may have attention deficit hyperactivity disorder (ADHD). Eyre dismissed the concept until one instance when his catcher tried to talk to him between pitches, and as soon as the conversation ended, Eyre could not recall what had been said between them. He received an ADHD diagnosis from an independent psychiatrist and began taking Concerta for games. In his first season with Toronto, Eyre saved 2 games in 15 games. In 2002, Eyre made 3 spot starts while also making 46 relief appearances for the Blue Jays, going 2–4 with a 4.97 ERA. San Francisco Giants (2002–2005) Eyre was selected off waivers from the Blue Jays by the San Francisco Giants in . He made the transition to the National League impressively as he had a 1.59 ERA in 21 games for the Giants. In 2003, Eyre appeared in 74 games with a 3.32 ERA. He was rewarded with a 2-year contract extension after the season. In 2004 Eyre appeared in 83 games while in 2005 he led the Majors in appearances, pitching in 86 games. He would eventually finish 30th in the NL MVP voting at the end of the season. Chicago Cubs (2006–2008) On November 18, , Eyre