"Our main objective has been to turn him into a 10-round fighter, but that is much easier said than done.
"We saw what happened with Sonny Bill [Williams]: he wasn't prepared to go 10 rounds - he wasn't even prepared to go nine - and he almost came unstuck. You can be damn sure we aren't going to make the same mistake."
Parker, who turned professional just over a year ago, said when he was amateur he did not believe he was capable of fighting or sparring 10 rounds.
"I have that belief now that I could last. It gives me a lot of faith in the goals that I have set."
Parker's here to promote his next fight, against Afa Tatupu (for the New Zealand National Boxing Federation belt), scheduled for October in Auckland. Parker will also fight in November, before four fights next year, which his promoters hope to take around the regions.
Parker has been matched against well-credentialled fighters in sparring, including undefeated Mexican Andy Ruiz. Despite his rather portly appearance, Ruiz (20-0) is rated as one of the hottest young prospects in the heavyweight division.
"The guy is a genuine puncher," said George Foreman recently of Ruiz. "I think in two-and-a-half years, maybe less - he will be heavyweight champ of the world."
Trading blows with Ruiz, a professional for six years, was a painful learning experience for Parker.
"The first time I sparred with Andy he gave me a good bash," says Parker. "I jumped in there and he chased me around the ring trying to knock my head off. I couldn't really fight back because I was lost; he was a beast and treated me like I was his son."
Parker was wounded, his pride as much as his body, but returned ready a few weeks later.
"In the next sparrings we were equal," says Parker. "I kept him away and he couldn't really come in. I was able to catch him a lot more. He showed me a lot more respect and it shows that the work is paying off."
Parker lives to a strict regimen in the United States. His alarm goes off at 5am, followed by a 9km road run. Breakfast, a quick nap and the Today Show follows ("Kevin has got me watching the news every day"), before more training, both in and out of the ring. Any spare time is spent hanging out with Barry's two teenage sons, though Parker has also got to enjoy some "treats".
He had ringside seats at the recent Floyd Mayweather fight, has rubbed shoulders with Mike Tyson and Larry Holmes and dined at the best table in the exclusive Picasso restaurant in Las Vegas, which has several original paintings by the artist on display.
A fight with Sonny Bill Williams (who holds the other New Zealand heavyweight belt) has been regularly mooted, and it is something that Parker would be happy to entertain.
"We are good friends," says Parker of Williams. "I stayed on the Gold Coast with him [and his family] when he was preparing for his Clarence Tilman fight. If the opportunity comes it would be good to get together and have a fight. In the ring it's definitely not friendly but outside we can be friends."
Parker appears to have his feet on the ground. He remains the humble, albeit fiercely confident, kid from Papatoetoe, yet to be sidetracked by the glitz and glamour of Sin City.
"I know I'm there for a reason and a purpose," says Parker. "And that keeps me focused even though it is hard to be away from home. I want to be [world] champ one day. That's what gets me up every morning."
