CINCINNATI — A trade that saved some money made the Cincinnati Reds’ next shortstop affordable.

The Reds sent center fielder Willy Taveras to the Oakland Athletics on Monday as part of a four-player deal, then agreed to a $3.02 million, one-year deal with Orlando Cabrera to become their starting shortstop. Both teams made a series of moves that changed the looks of their rosters.

Along with Taveras, the Reds sent infielder Adam Rosales to the A’s for infielder Aaron Miles and a player to be named. Oakland was busy as well, agreeing with outfielder Gabe Gross on a $750,000, one-year contract and claiming infielder Steve Tolleson off waivers from Minnesota.

Once the A’s got Taveras, they designated him for assignment, along with left-hander Dana Eveland, to create space on their 40-man roster for the newcomers.

“I think we’ve been able to do some things to improve our club where we weren’t too sure we would be in position to do that,” Reds general manager Walt Jocketty said. “A lot of it was being patient and waiting for the market to drop to our level, where we could afford to do some things.”

Cabrera got a deal that pays him a $1.25 million signing bonus and $770,000 salary this year. The agreement includes a $4 million mutual option for 2011. If Cabrera declines it, he gets a $500,000 buyout. If he accepts it and the team declines, he receives a $1 million buyout.

Cincinnati traded shortstop Alex Gonzalez to Boston last August, leaving the position to Paul Janish, a solid defensive player who batted .211.

Several teams were interested in Cabrera as a second baseman, making the Reds a more attractive destination because he could play his natural position.

“A little bit,” Cabrera said. “But I think the challenge of the Reds is better for me.”

The 35-year-old shortstop played for Oakland and Minnesota last season, batting a combined .284 with 36 doubles, nine homers and 77 RBIs in 160 games. Cincinnati expects to bat him second, with 25-year-old Drew Stubbs in line to bat leadoff now that Taveras is gone.

“I’m going to do everything I can, even if I have to change my name to one Ocho,” Cabrera said, referring to Bengals receiver Chad Ochocinco.

The Reds thought they’d filled their long-standing hole at the top of the batting order when they signed Taveras to a two-year deal, but he struggled with injuries last season, batted .240 and had an on-base percentage of only .275 with 25 stolen bases. A free swinger, Taveras drew only 18 walks in 435 plate appearances.

Cincinnati saved $4 million by getting rid of Taveras, who was due that much in the final year of his deal. That will cover Cabrera’s deal and part of Miles’ contract, which pays him $2.7 million this season.

The 33-year-old Miles batted .175 in 84 games with the Cubs last season, when he had shoulder and elbow injuries. The Cubs traded him to the A’s in December along with Jake Fox as part of a five-player deal.

Jocketty came from St. Louis, where Miles was part of the Cardinals’ 2006 World Series champions. He batted .318 for St. Louis in 2008, and is pegged as a backup infielder in Cincinnati.

“He played an important role in that club in 2006 when (David) Eckstein got hurt late in season and we were without a shortstop,” Jocketty said. “He played flawlessly at short. He’s played all the positions except catcher and first base.”

The A’s signed Gross to a deal that includes several incentives besides his base salary. He would get $50,000 each for making 400, 450, 500 and 550 plate appearances. Gross batted .227 with six homers and 36 RBIs in 115 games with Tampa Bay last season. He also has played for Toronto and Milwaukee.

Tolleson played at Double-A and Triple-A last season, batting combined for a .266 with 27 doubles, eight home runs, 40 RBI and 13 stolen bases in 130 games.