He was selected in the second round of the 1986 amateur draft by the Milwaukee Brewers out of Miami-Dade College. He immediately joined the Helena Gold Sox in the Rookie-level Pioneer League, then went 4-6 with a 5.92 ERA over 18 appearances (10 starts). He struck out 40 in 65.1 innings pitched and collected a 1.71 WHIP. Milwaukee promoted him to single-A for the 1987 campaign, with the Midwest League Beloit Brewers. Drahman went 6–5 with a 2.16 ERA in 46 appearances. He had 18 saves and struck out 60 in 79 innings with a 1.08 WHIP.\n', '

In 1998, Drahman played high-A level with the Stockton Ports, going 4–5 through 44 relief appearances with a 2.02 ERA and a 1.35 WHIP. He struck out 50 batters in 62.1 innings, but did not earn a promotion, starting the following season again with the Ports. He went 3–2 in a dozen appearances with a 3.25 ERA before earning a callup to the AA level, for the El Paso Diablos in the Texas League. He went 3–4 and his ERA ballooned to 7.26 in 19 relief appearances before the Brewers traded him to the Chicago White Sox for Jerry Reuss. Drahman was sent back to the A+ level, and played with the Sarasota White Sox in the Florida State League. He went 0–1 over seven games, with a 3.24 ERA.\n', '

Drahman joined the Birmingham Barons in the double-A level Southern League for the 1990 campaign, spending the entire season with the club. He had a 6-4 record over 50 games (49 in relief), along with a 4.08 ERA and a 1.26 WHIP, striking out 72 in 90.1 innings pitched. In 1991, he opened the season with the White Sox. He blew a save in his first appearance then gave up five earned runs in 0.2 innings his next time out before settling down to earn a win on April 21. In that contest, he struck out one and allowed no hits or walks in the ninth before Lance Johnson hit a walk-off single in the bottom half for a 5–4 win over the Detroit Tigers. Overall, he played 28 games for the Sox, going 3–2 with a 3.23 ERA and a 1.109 WHIP, striking out 18 in 30.2 innings.\n', '

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