The Dodgers came very close to signing catcher A.J. Pierzynski to a one-year deal before he re-signed with the White Sox. Chicago added a second year to their offer and Pierzynski signed a two-year, $8 million deal. A source with knowledge of the situation, speaking on the condition of anonymity, confirmed that the Dodgers were close to a deal last week that would have paid Pierzynski in excess of $4 million.