The Boston Red Sox bolstered their bullpen Tuesday, acquiring closer Scott Williamson from Cincinnati for a minor league pitcher, a player to be named and cash.

The team they are chasing in the AL East, the New York Yankees, made two deals Tuesday, including sending outfielder Raul Mondesi and cash to Arizona for outfielder David Dellucci and a two minor leaguers.

Williamson, the NL Rookie of the Year in 1999, converted 21 of 26 save opportunities for the Reds this season.

Red Sox general manager Theo Epstein said he envisions Williamson as a setup man for closer Byung-Hyun Kim.

The deal was one of five made Tuesday before Thursday’s trading deadline.

The White Sox acquired left-hander Scott Schoeneweis and a minor leaguer from Anaheim for reliever Gary Glover and two minor leaguers.

The New York Mets traded seldom-used infielder Rey Sanchez to Seattle for minor league outfielder Kenny Kelly.

And, the Yankees also traded right-hander Dan Miceli to Houston for a player to be named or cash.

The Reds’ trade was their first since firing general manager Jim Bowden Monday.

“We’ve been talking to the Reds on and off for a week or two,” Epstein said. “Once they made their move in the front office, things really accelerated … we got down to business very quickly.”

The Reds got left-hander Phillip Dumatrait, 22. He was 7-5 with a 3.02 ERA in 21 games at Class A Sarasota.

Epstein said the Sox are looking to acquire another starter before the trading deadline.

“A great opportunity came along and we feel that we made our team a lot better,” he said. “We’re not done.”

Mondesi, 32, is joining his fourth team in five seasons. He returns to the National League, where he was rookie of the year with the Dodgers in 1994.

Mondesi is hitting .258 with 16 homers and 49 RBIs in 98 games this season, but had only five hits in his last 27 at-bats.

In addition to Dellucci, who was hitting .242 with two homers and 19 RBIs, the Yankees also got right-hander Bret Prinz and catcher John Sprowl. Prinz was assigned to Triple-A Columbus, while Sprowl will report to Class-A Battle Creek in the Midwest League.

In addition to Schoeneweis, the White Sox acquired right-hander Doug Nickle and they sent right-hander Scott Dunn and left-hander Tim Bittner to Anaheim.

Schoeneweis, the only lefty in the Angels’ bullpen, made 47 starts the previous two years but was used exclusively in relief this season. He is 1-1 with a 3.96 ERA in 39 appearances this season.

The 29-year-old has a 28-31 career record with a 5.10 ERA in 183 games, including 74 starts.

Nickle was 2-2 with four saves and a 1.48 ERA in 34 relief appearances with Triple-A Salt Lake City. He will be assigned to Triple-A Charlotte.

Glover, 26, was 1-0 with a 4.54 ERA in 24 relief appearances with Chicago.

Dunn, 25, was 3-1 with a 1.69 ERA in eight relief appearances with Double-A Birmingham after being acquired July 6 in a trade with Cincinnati.

Bittner, 23, went 4-4 with a 3.40 ERA in 10 starts for Single-A Kannapolis and 3-3 with a 3.60 ERA in 17 appearances for Single-A Winston-Salem.

Sanchez was hitting .207 with 12 RBIs in 174 at-bats this season with New York. He has one-third of his $1.3 million salary left for this season, and the Mariners will pay a portion of that. With shortstop Carlos Guillen hobbled by a groin injury, the Mariners needed some help.

Kelly was hitting .246 with 13 homers and 37 RBIs in 96 games at Triple-A Tacoma. The Mets assigned him to Triple-A Norfolk.

Miceli, 32, was taken off the Yankees’ roster Friday when he was designated for assignment, clearing a spot for Nick Johnson to come off the disabled list.