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Hubbard flew to Green Bay Sunday afternoon after agreeing to terms on a free-agent contract with the Packers shortly after the draft concluded Saturday.
"I didn't know it could be a problem because we had all the issues fixed," Hubbard said. "I think the big problem was somehow, some way the papers didn't get to all the teams. But, oh well."
Hubbard said he had been cleared by Charles Brown, chief medical officer at Piedmont Heart Institute in Atlanta and the Falcons' cardiologist since 1992.
"My heart's big because I'm big," said Hubbard, who indicated it was discovered on his EKG at the combine. "There's nothing wrong with it at all. This is more than 85% of the league. Dr. Brown looked at me and cleared me."
He was carrying papers from Brown for the Packers' medical staff. He must pass a physical before officially joining the team.
"It's going to pass," Hubbard said. "Not too much worry. I'm fine. I've been playing in the worst conditions the last four years in the heat of Alabama. I've been playing sports my whole life. I'll be OK.
"Situations happen. I wasn't drafted. I'll have to go a different route. Teams don't want to take risks. They don't want to write off on people."
Hubbard, 6 feet 6 inches and 257 pounds, was projected as a mid-round draft choice. A fourth-year junior, he started the past two seasons as strong outside linebacker in the Crimson Tide's 3-4 defense.
He finished with 83 tackles (18 for loss) and 10 sacks in 36 games, including 26 starts.
"I talked to Eddie (Lacy) last night," said Hubbard. "He said, 'Come in here, you know how to work, do what you do.'"