Melbourne, Australia, 17 January 2012 | AAP

Former world No.4 Jelena Dokic has thrashed Russian Anna Chakvetadze 6-2 6-1 in the first round of the Australian Open.

The newly chilled-out Dokic is eyeing a return to the world top 20 for the first time in eight long years.

On a dramatic day when Samantha Stosur and Jarmila Gajdosova fell at their home grand slam, Dokic made it look easy against Russian Anna Chakvetadze.

For a player often noted in her prime as much for her brooding intensity as her stunning strokeplay, Dokic cut a remarkably relaxed figure in the aftermath of her 6-2 6-1 win over Chakvetadze.

Both Dokic and the Russian are former top five players who have fallen on hard times in recent years.

And the Australian can now see a way back to the pointy end of the world rankings.

“First of all you want to be healthy and have a full year with no injuries,” said Dokic, whose current world ranking stands at 64.

“If I can do that I think it will be a good year, so that’s the most important thing at the moment.

“If all goes well, hopefully top 20.”

A key figure in the 28-year-old Dokic’s late-career resurgence is new coach Louise Pleming, who has the happy knack of keeping things in perspective.

“You have to just chill a little bit,” said Dokic.

“Not just me, but things in general and things come a lot easier when you do that.

“That’s something I’ve been on working with Louise because you’re going to have bad days.

“You can’t play well 365 days a year.

“Sometimes you have to win ugly but sometimes you’re also going to lose matches.”

Gajdosova, whose career ranking reached No.24 last year, looked a tortured soul as she tried to explain away her 6-4 6-2 loss to No.27 seed Maria Kirilenko from Russia. She mixed 42 unforced errors with 28 winners against the steady Kirilenko.

“You start questioning the shots before you even hit them,” said Gajdosova.

“And then you make errors in the end just because you change your mind on what you usually do and what you want to do.”