Drafted by the New York Mets out of Junípero Serra High School in the first round of the 1985 amateur draft (#20 overall), Jefferies hit .331 in his first year in the minor leagues, moving from Kingsport of the Appalachian League (rookie) to Jackson of the Texas League (AA) in two years. He was named "Baseball America"'s Minor League Player of the Year for both 1986 and 1987, becoming the first player to receive that distinction in consecutive years. He hit .367 with 20 home runs, 48 doubles and 101 RBI for Jackson in 1987, earning Jefferies a brief call-up from the New York Mets at the end of the 1987 season. He went 3 for 6 in 6 games, at the age of 19, making him the youngest player in the Major Leagues that season.