Acosta, a 29-year-old right-hander, went 1-1 with a 3.00 ERA in 12 appearances in April and May, his only other stint with the club this season. He is available Friday night for the second of a four-game series at Dodger Stadium.
Used heavily at the start of the season, Nieve had a 3.46 ERA in April but saw his ERA shoot up to 9.75 in May. A day before being designated, he allowed a walk-off hit to the D-backs in a 4-3, 14-inning loss in Arizona.
Acosta was 2-3 with five saves and a 3.47 ERA in 28 games at Triple-A Buffalo. He didn't allow a run in his last 6 2/3 innings in the Majors, going back to May 11.
The Mets' bullpen ranks 10th in the Majors with a 3.59 ERA.