The Astros took University of North Carolina right-hander J.B. Bukauskas with the No. 15 overall pick in the first round and Texas A&M right-hander Corbin Martin -- a former teammate of Ivey -- with the No. 56 overall pick in the second round.
The Draft concludes on Wednesday, with exclusive coverage of Rounds 11-40 beginning on MLB.com at 11 a.m. CT.
Tuesday will have selections from Rounds 3-10. Here is a pick-by-pick look at the Astros' Day 2 Draft selections:
Round 4: RHP Peter Solomon, Notre Dame
The Astros took another college arm in the fourth round, nabbing Solomon with the 121st overall pick.