Anderson, 31, whom the Royals obtained from Cleveland in an August trade, agreed to a two-year, $6.5 million contract. He went 5-1 with a 3.99 ERA in seven starts for Kansas City last season.
Leskanic, 35, agreed to a one-year, $1.5 million deal with a team option for 2005. After Kansas City obtained him in July from Milwaukee, he went 1-0 with a 1.73 ERA in 27 relief appearances.
Randa, 33, also agreed to a one-year, $3.75 million contract with a mutual option for 2005. He hit .291 last season and tied a career high with 16 homers. His .344 average after the All-Star break was third-best in the American League.