But ask the fourth-year GM what he thinks has been his most meaningful transaction, and his answer will surprise you.
The blockbuster draft-day trade with the Browns to acquire Mark Sanchez with the fifth overall pick?
The Braylon Edwards trade?
The draft-day deal to get Shonn Greene?
None of the above.
"The one that stands out to me is re-signing Brandon Moore," Tannenbaum said, referring to the Jets' right guard. "That's the one that really meant a lot."
Not to minimize the deals to get Sanchez, Edwards and Greene - or his decision to hire Rex Ryan to replace Eric Mangini as coach - but Tannenbaum is most proud of the Moore deal because it was the one that looked as if it might not happen.
The Jets had attempted to rework Moore's deal in the offseason, but to no avail. They wound up releasing him, but Tannenbaum remained intent on keep his offensive line intact.
"We knew we wanted to run the ball, and we felt that Brandon was an important piece of that plan," Tannenbaum said. "That's why I thought it was so important."
I asked him if his handling of the Pete Kendall situation in 2007 played into his concerns, and Tannenbaum insisted it didn't. But he won't ever forget the damage done by his unwillingness to address Kendall's contract during the offseason and the preseason. That intransigence led to Kendall's release, and the Jets paid for that move dearly. In the opener that year, Chad Pennington suffered a sprained ankle because of some shoddy blocking against the Patriots, and the Jets wound up 4-12.
Moore was keenly aware of the situation and thought he'd wind up in a similar position.
"I understand it was a business, and there were no hard feelings," he said. "I have a lot of respect for Mike and the people who run this team, but I was also looking forward to free agency. I told my wife during that time that I wouldn't want to leave here, look back and see this team in the Super Bowl and not be a part of it. Fortunately, it's worked out."
Credit Tannenbaum with setting the stage, and not just with the Moore deal.
His hiring of Ryan, his aggressiveness in making the trades to acquire Sanchez and Greene, and his successful pursuit of free agents Bart Scott, Jim Leonhard and Marques Douglas have been key factors in the Jets' run to the conference championship game.
"It's a team effort,'' Tannenbaum said, "and I'm just a part of that."
Don't let him kid you. He's a big part of it.