He moved up to the double-A level London Tigers near the end of the season in the Eastern League, where he had less success, going 0–4 over five starts with a 6.26 ERA and a 1.87 WHIP.

Edmondson spent two and a half seasons with the Binghamton Mets in the Eastern League, appearing in 76 games and making 35 starts.

Near the end of May in 1997, he finally made the jump to triple-A, joining the Norfolk Tides in the International League, making starts in four of his 31 appearances and going 4–3 with a 2.90 ERA and a 1.45 WHIP with 65 strikeouts in 68.2 innings pitched.

The Rule 5 draft necessitates that any player selected must remain on the major league roster for the entire season or else be subject to getting reclaimed by the original club.

Edmonson began the campaign on Atlanta's opening day roster, and made 10 appearances for the Braves during the first two months of the season.

From June 8 through July 12, he appeared in a dozen games, holding opposing batters to a sub-one WHIP and a 1.47 ERA and striking out 13 over 18.1 innings.

He earned his first win of the season on April 27, pitching 3.1 innings of shutout ball against the Chicago Cubs, striking out three and hitting two doubles with an RBI.

He made his return in 2001, joining the high-A Brevard County Manatees in the FSL on opening day, and going 5–2 with a 1.73 ERA over 16 appearances, with 21 strikeouts in 26 innings and a 1.04 WHIP.