Fury has that. At 1.98m, he is a big man, but, while nothing is guaranteed in the world of professional boxing, the 1.93m Parker should have an easier night of it this time.
He will have a clear advantage in terms of hand and foot speed and the ability to punch in combinations. Even trainer Barry, in the business of talking up opponents pre-fight, has conceded Fury should in theory suit Parker better.
"He's definitely a bigger challenge for the fact that he's six foot six," Barry said. "Will he bring the pressure that Andy Ruiz brought? Probably not. But I've studied him for some time and I feel he's getting better with every entry to the ring.
"He's very well coached by his father Peter, he's got a tremendous amateur pedigree - he's a very difficult, very awkward guy who uses his height and reach very well. I don't see this being an easy fight for us, I see this being a serious challenge and one we'll take very seriously."
The lessons of the Takam training camp - overlong at 12 weeks - have stayed with the Parker team. The 25-year-old has eased off training for the past fortnight in order to give his body a rest and will start sparring next week, the first of what is effectively now an eight-week camp.
Parker also had issues during his camp prior to the Ruiz Jr fight, including the emotional upheaval of the birth of his first child and other family celebrations, and will be hoping for a smoother, more productive camp this time.
"We feel very good about where his condition is at and where his confidence is at," Barry said.
"We've put a very good game plan in place. In this fight you'll see different tactics to what we saw in the last fight where we saw Joe mostly on the back foot. In this fight against Fury I think Joe will have to make the fight. He'll have to be the aggressor, the guy coming forward because I don't see that in Hughie's style."