I remember the Pettitte negotiations well, Andy has been my favorite player since he came up. I thought they should have signed him to an extension earlier, but health problems scared them off.
Pettitte asked for time to weigh his options after 2003, and Cashman let him. In that time, Houston made a gigantic pitch him, based on living back in Texas. When the Yankees got involved it was too late, because despite their efforts Houston had been sold to him. Point being I really think it was more the fact that he wanted to play in Houston than Yankees folly.
There wasn't a lowball offer to Pettitte (like Boston's 3/27 to Damon), and there was a higher final offer than the contract he signed with Houston (unlike Boston's unwillingness to budge from 4/40).