Rhymes, a junior from Monroe, was chosen in the 30th round by the New York Yankees. Hanover, a senior from Kernersville, N.C., was selected in the 33rd round by the Detroit Tigers.
Rhymes, the 2012 South-eastern Conference Player of the Year and a First-Team All-American, is leading the nation in hitting with a .452 (99-for-219) average. He has produced 11 doubles, four homers and 52 RBIs this season.
Hanover is No. 10 in LSU career annals with 271 hits, and he is the Tigers’ all-time leader in sacrifice bunts with 36. He is batting .288 (62-for-215) this season with 13 doubles, one homer and 28 RBI.
Also selected Wednesday were LSU signees Will LaMarche (18th round, Minnesota) and Alex Bregman (29th round, Boston).
LSU first-team All-America pitcher Kevin Gausman was chosen in the first round Monday by the Baltimore Orioles. Also selected Monday in Compensatory Round A were LSU signees Joey Gallo (39th selection, Texas Rangers) and Jesmuel Valentin (51st selection, Los Angeles Dodgers).
LSU shortstop Austin Nola (fifth round, Miami) and pitcher Nick Goody (sixth round, New York Yankees) were selected during Day 2 of the draft Tuesday.
Also selected Tuesday was LSU signee Hayden Jennings, an outfielder from Evangel High School in Shreveport, who was chosen in the sixth round by the Washington Nationals.