The Browns traded up in the fifth round on Saturday for the 160th overall pick, which was used to select Florida State OL Roderick Johnson.
Cleveland gave the Jets picks No. 181 (fifth round) and 188 (sixth round) and receved picks 160 and 224, a seventh-rounder.
The Browns have made four trades thus far in the draft, including two moves Day 1 to net three first-round picks. They also traded up in the fourth round earlier Saturday to take Houston defensive back Howard Wilson.
The Browns have three more picks at Nos. 185, 224, 252.
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