We've had some questions about what, exactly, non-tendering means. Since Astros County is not an elitist blog with abbreviations and formulas of which you've never heard, I'll tell you - because no one else will.
MLB teams have to offer contracts to players by tomorrow night. It can't be less than 80% of the 2008 salary and bonuses, and it can't be less than 70% of 2007 salary and bonuses. If the team thinks even 80% of 2008 salary is too high, they may choose to non-tender him - or simply to not offer that player a contract. You might do this if a player was eligible for arbitration, but that salary would be too high. If the player is non-tendered, they are a free agent and can negotiate with all 30 teams.
As it stands, Brandon Backe and Ty Wigginton are in danger of being non-tendered.
So basically, since the Astros paid Backe $800,000 last year, they can't offer him a contract for less than $640,000. If they wanted to offer him less than $640,000, they would non-tender him and then try to resign him over the 29 teams that might want him (but I think the Yankees are all set, thanks).