American superstar Serena Williams blew her Swedish opponent off centre court at the Hobart International on Monday night in her first match since last year's US Open.

Williams, 25, said she was rusty, and it showed in the first set of her 6-4 6-0 victory.

The seven-time Grand Slam champion powered her way to a 5-0 lead in the opening set before a courageous Sofia Arvidsson clawed her way back by winning four consecutive games.

Williams closed out the set on serve, and then used some outstanding service returns and missile-like forehands to steamroll the world No.63 in the second set.

Ranked 95th and on the comeback from ankle and knee problems, Williams said her best was yet to come.

"The whole match I didn't play my best," Williams said.

"I'm a little rusty because I haven't played since the US Open.

"I only played four tournaments in 2006, so I think there's a little bit of rust coming out."

Williams wants her serve working better before she heads to Melbourne for the Australian Open next week.

"I just want to work on my serve and be able to serve a little faster by the time I get to Melbourne," she said.

"There is so much more I have to do.

"I have to go home and study and I know my mum is going to tell me some things I don't want to hear but I know I need to hear.

"This is just the start, I'm taking it one match at a time."

Williams is scheduled to play Czech Lucie Safarova, ranked No.41, in the second round on Tuesday.

Alicia Molik won her first round match against Croatian Jelena Kostanic 4-6 6-1 6-2 and will meet sixth seeded Ukrainian Alona Bondarenko in the second round on Tuesday.

The Australian took control early in the second set and dominated from there, Kostanic managing to hold service just three times in the final two sets.

"I made too many errors in the first set, and Jelena hit too many winners," Molik said.

"But I was confident I would tighten up as the match went on.

"The windy conditions made it difficult for both players.

"In the second set I started to use the wind smartly and move her round the court more.

"I'm happy with the result - she got three games in the last two sets, I can't really complain about that.

"I'm looking forward to the second round."

Defending Hobart champion Michaella Krajicek became the first major casualty on Monday when beaten by France's Severine Bremond in the opening round.

The match went to three sets, with Krajicek, ranked No.35 in the world, looking comfortable in winning the first 6-3.

Bremond, ranked No.39, then received treatment for leg complaint before amazingly bouncing back to claim the next two sets 6-1 6-0.

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