Very quietly, the Tampa Bay Buccaneers have given safety Tanard Jackson a contract extension and a nice raise for the rest of this season.

The Bucs now have Jackson under contract through the end of the 2012 season. Jackson was suspended in September 2010 for one year for violating the NFL’s substance abuse policy. His contract initially was set to expire after the 2010 season, but league rules for the suspension meant that the remainder of Jackson’s contract “tolled’’ over to 2011.

Jackson was reinstated after missing the first five games and had been scheduled to earn $705,000 for the remainder of this season. But Jackson’s new deal calls for him to earn $1 million this season.

The Bucs are showing some faith in a player who has had problems by adding 2012 onto his contract, but they’ve structured the deal with some incentives for Jackson to stay out of trouble.

In 2012, Jackson’s base salary will jump to $2 million. He also will get a $200,000 roster bonus on the first day of the league year and will earn a $50,000 bonus for every game that he’s on the 53-man roster. Jackson’s cap figure for 2010 will be $2.95 million.