Updated

By Ian Ransom

Williams, whose last grand slam ended in a huge fine and a two-year probation after a tirade at a line judge at Flushing Meadows, denied she had changed her on-court style to protect herself from the game's moral guardians.

"No, I don't think I was quiet at all. I felt like I pumped my fist a little bit. I feel like I was definitely being who I could be. That's all I can do," said Williams, whose loudest on-court statement was a chunky diamond medallion from her signature jewelry line.

"I don't know whoever got fined like that. People said worse, done worse. I just thought it was a bit much," she said.

"I always said what I did wasn't right, but I turned that around and I'm actually raising $92,000 to educate ladies, women, also for my school in Africa.

"Also I'm giving some money to Haiti, as well, because (of) the recent things," added Williams, referring to the disastrous earthquake that hit the Caribbean country last week.

Williams, who was troubled by a sore knee in a straight-sets loss to Russia's Elena Dementieva in Friday's Sydney International final, wore heavy-strapping on her right leg in the match.

She appeared in no discomfort, however, in dispatching the 72nd-ranked Radwanska, the younger sister of world number 10 Agnieszka.

"Yeah, I've been having it strapped all week, all last week as well," she said. "So just keep it up and making sure I'm able to keep moving as best as I can.

"It's to support my hamstring ... just to make sure that I don't have a Sydney moment."

Williams's win preserved her record of never being knocked out of the first round of a grand slam.

"I was a little nervous today because that's always on the back of my mind," she said. "Records are meant to be broken. So I'm like, 'God, I hope this record is not to be broken ...' I want to just keep that up."

Williams will next play the winner of the match between fellow American Jill Craybas and Czech Republic's Petra Kvitova.

(Editing by Nick Mulvenney)