In the free-agent game, the Los Angeles Dodgers have two down and seven to go.

Fernando Valenzuela and Jay Howell, both eligible for free agency, have agreed to new contracts with the World Series champions. Valenzuela agreed to a one-year contract for $1.85 million and Howell agreed to a two-year deal for a guaranteed $2.25 million.Meanwhile, pitcher Ron Davis of San Francisco filed for free agency Tuesday, the Major League Baseball Players Association said, raising the total to 51. Eligible players have until Friday to file.

Also, infielder Dickie Thon of the San Diego Padres filed a demand to be traded Tuesday. The Padres must trade him by March 15 or he becomes a free agent.

Valenzuela, injured for much of the season, agreed late Monday to a one-year contract for $1.85 million, a $200,000 pay cut. He completed a three-year, $5.5 million contract in 1988.

Valenzuela was 5-8 with a 4.24 earned-run average this season in 22 starts. He went on the disabled list on July 31 and returned Sept. 26, making two appearances in the season's final week.

Dick Moss and Tony DeMarco, Valenzuela's agents, met Monday with Dodgers general manager Fred Claire. Moss said he was not seeking another multiyear deal.

"I think it's to everybody's benefit to see how Fernando comes back next year," Moss said. If he returns to form, Moss said Valenzuela would try to get a multiyear contract next year.

Howell, involved in controversy during the National League playoffs because of using pine tar on his glove, agreed Monday to a two-year contract for a guaranteed $2.25 million. Howell, who made $595,000 in 1988, gets a $250,000 signing bonus and will make $800,000 next year and $900,000 in 1990. The Dodgers have an option for 1991 at $1.05 million but Howell will get a $300,000 buyout if it is not exercised.

Howell was 5-3 this season with a 2.08 ERA and 21 saves, eighth in the NL.

Los Angeles has seven potential free agents. Shortstop Alfredo Griffin has filed and pitchers Jesse Orosco, Alejandro Pena and Mario Soto, infielder Steve Sax and outfielders Mickey Hatcher and Mike Marshall are eligible.

Davis was 1-1 for the Giants with a 4.67 ERA in 17 innings over nine games after pitching in the minor leagues most of the year.

Thon batted .264 with one homer and 18 RBI in 258 at-bats.