At the end of spring training in 1961, the Cubs decided no longer required Drabowsky and traded him along with Seth Morehead to the Milwaukee Braves for Daryl Robertson and Andre Rodgers. Milwaukee did not have room for him in their rotation, though, and used him exclusively in relief, where he had an 0–2 record and a 4.62 ERA in 16 games. After Drabowsky gave up four runs in the sixth inning of a 10–8 loss to the Cincinnati Reds on June 8, Milwaukee banished him to the minor leagues and never bothered to call him up again the rest of the season. He finished the year pitching for the Louisville Colonels of the American Association, where in 20 games (nine starts), he had a 9–6 record but a 4.75 ERA, with 54 strikeouts in 106 innings pitched. Milwaukee left him unprotected from the Rule 5 draft after the season, and he was selected by Cincinnati. He started 1962 with the Reds, who used him both as a starter and a reliever. In 23 games for them (10 starts) through August 4, he went 2–6 for them with a 4.99 ERA. On August 13, the Kansas City Athletics acquired him for cash. He appeared in 10 games (three starts) for Kansas City the rest of the year, going 1–1 with a 5.14 ERA. Drabowsky's combined stats on the season were a 3–7 record, a 5.03 ERA, and 75 strikeouts in 33 games (13 starts).