While Heath and Leesman are no longer at risk of being taken by another club, several White Sox Minor Leaguers, including outfielder Jordan Danks and right-hander Terry Doyle, were left unprotected.
Danks, the younger brother of Chicago starter John Danks, is widely considered to be the best defensive outfielder at any level in the organization. He played in 134 games for Triple-A Charlotte in 2011, his second year at that level. The 25-year-old batted .257 with 65 runs scored, 44 extra-base hits and 65 RBIs.
With a stellar showing in the Arizona Fall League, Doyle seemed to put himself in position to be strongly considered for a 40-man roster spot. The 26-year-old right-hander posted a 1.98 ERA in eight AFL starts, walking five and striking out 22 in 27 1/3 innings.
Doyle split the 2011 season between the Class A Advanced and Double-A levels, where he combined to go 8-10 with a 3.07 ERA in 26 starts.
After pitching in Triple-A in 2011, Heath could be ready to make an impact in Chicago as early as next season. He split time as a starter and reliever, totaling 102 2/3 innings for Charlotte. Heath had a 4.73 ERA and struck out 117.
Sixteen of the final 18 appearances Heath made last season came as a starter. He has been pitching in the Venezuelan Winter League this offseason, going 2-2 with a 2.37 ERA and 29 strikeouts in six starts.
Heath, 26, has been in the organization since April 22, 2010, when the White Sox signed him as a Minor League free agent. He began his professional career in the Braves' farm system.
Leesman spent the year with Double-A Birmingham, where he went 10-7 with a 4.03 ERA in 27 starts. The 24-year-old lefty struck out 113, but also walked 83 in 152 innings. He was recognized as a midseason All-Star in the Southern League.
An 11th-round pick in the 2008 First-Year Player Draft, Leesman has made 85 appearances (83 starts) in four seasons with the organization.
The additions of Heath and Leesman to the 40-man roster still leave the White Sox with four openings. By leaving room on the roster, the White Sox have the flexibility to add free agents, other acquisitions or players they choose in the Rule 5 Draft, which will take place on Dec. 8.
Jenifer Langosch is a reporter for MLB.com. Read her blog, By Gosh, It's Langosch, and follow her on Twitter @LangoschMLB. This story was not subject to the approval of Major League Baseball or its clubs.