Alsup, a right-hander selected in the 18th round by the Colorado Rockies in last month's MLB Draft, has made one start for Class A Tri-City (Wash.) Dust Devils, recording no walks and five strikeouts in four innings of work.
Ott, a right-hander chosen in the 13th round by the Boston Red Sox, has been assigned to the Class A Lowell (Mass.) Spinners and has not yet made an appearance on the mound.
Alsup, undrafted out of Ruston (La.) High School, posted a 12-6 career mark in four seasons at LSU with a 4.77 ERA in 149 innings. Alsup, who fired an SEC Tournament shutout against Ole Miss in 2010, was 6-5 for the Tigers this season with a 4.66 ERA and one save in 65.2 innings.
Ott, a product of Holy Cross High School in New Orleans, is LSU's all-time saves leader with 33 in his three-year career. He was 1-3 this season with a 2.60 ERA in 27.2 innings, recording seven walks, 27 strikeouts and six saves.
Ott, who was undrafted out of high school, was named SEC Freshman of the Year and a second-team all-American in 2009, when he was 4-2 with a 2.50 ERA and an LSU single-season record 16 saves.