Leibrandt, 33, was 5-11 with a 5.14 earned-run average in 33 games with the Royals last season. He has an overall record of 92-78, with a 3.77 ERA. Luecken, 29, who spent most of last season in the minors, appeared in 19 games with the Royals, posting a 2-1 record with one save and a 3.42 ERA.
Perry batted .252 with four home runs and 21 runs batted in last season.
The minor league pitcher in the deal was Jim Lemasters, who had a 7-5 record and a 2.19 ERA for Greenville, N.C., Atlanta's affiliate in the double-A Southern League.