Andy Murray is a pretty tough judge of his own performances so when he gives himself more or less top marks for his first week at Melbourne Park, you know he is satisfied.

Three straight-sets wins mean he should be relatively fresh going into the business end and that, as much as anything, could be crucial to his hopes of a second straight Grand Slam title.

The Scot tomorrow takes on Gilles Simon of France in the fourth round and, with his section of the draw opening up nicely, it is hard not to see him making it through to at least the semi-finals, where Roger Federer is seeded to be waiting.

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"I think in terms of the results, it's nine or 10 out of 10 because I haven't had any long matches and especially on the day when it was extremely hot, it was a quick match, and it was efficient in terms of the way I'm playing," Murray said.

Murray would not be Murray, though, if he did not have a few things he was not happy with and after his 6-3, 6-4, 7-5 win over Ricardas Berankis of Lithuania yesterday, he said he felt his ball-striking could improve.

"All the courts at the slams play differently," he said. "Very rarely do you get two courts that play exactly the same so sometimes when you switch courts from match to match that can throw the rhythm off a little bit. And, I haven't played a match on the outside courts. I've practised on them but players have said they're extremely fast courts; whereas the show courts tend to be a little bit slower. So that can sometimes play a part in it.

"I'd like to play better, that's for sure. I don't know exactly how much better I need to play or how well I'm playing right now but I'll certainly need to improve in the second week if I want to win it."

Turn back the clock a year and Murray was in a similar position, losing a set in round one but cruising through his next two matches to reach the last 16 in good shape. The enormous difference 12 months on is that he has now won a Grand Slam title. That knowledge and confidence, combined with his form, means that he is in a more relaxed state of mind, which can only stand him in good stead.

"It's felt pretty similar, to be honest," he said. "I was certainly very nervous before the first match and when the conditions are like they were before the second match as well, you're also going be nervous because anything can happen on days like that.

"I'd say it feels the same as other slams. I just hope that maybe in the second week I'll feel a bit more comfortable and a bit more experienced, having won a slam and won the big matches. That will help."

As he did last year, when he was edged out by Novak Djokovic in an epic semi-final, Murray has been practising off-site, at nearby Kooyong, where the Australian Open was played until 1988.

His coach, Ivan Lendl, has been reminding him that it is how he plays on match day that matters, that the days in between are about getting his body in shape for the battles to come.

"So long as you fire your body up and you move your feet properly and concentrate during the practice it doesn't matter how you hit the ball," Murray said. "The more matches you play on the courts you're going to feel better, and it's just good having someone like him to re-emphasise those points on practice days."

Simon and Gael Monfils ran each other ragged late into the night before the former won in five sets. Murray, doubtless watching on television with his feet up, must have been absolutely loving it. It was an utter war of attrition, full of epic rallies, with one lasting 71 shots. It will be a wonder if Simon can walk properly today.

Murray has won his last nine matches against Simon and knows he has the beating of the Frenchman, even before taking into account the incredible effort he put in against Monfils.

"It helps, obviously, if you have a good record against players," Murray said. "It'll give you confidence but there are always times where guys have good records against players and lose.

"So you need to make sure that you're not overconfident, that you stick to your game plan and do the things that have worked well against him in the past. He's the sort of guy that you need to make sure you're extremely patient against because if you're not he'll force you into making mistakes and going for too much."

No man in the open era has followed up their first Grand Slam title by immediately winning another next time out. Murray knows his history but is confident he can break the mould, helped, perhaps, by his draw opening up rather kindly.

The defeat of former US Open champion Juan Martin del Potro by Frenchman Jeremy Chardy yesterday means either Chardy or Italy's Andreas Seppi will make their first Grand Slam quarter-final. Provided Murray gets past Simon, he may be well set.

It is the kind of fortune usually reserved for the No 1 seed, something Federer himself experienced many times when he was in his pomp. The second-seeded Swiss's draw this year is far from easy but he looked awfully good yesterday in knocking out Australia's last hope, Bernard Tomic.

Tomic had tried out a bit of trash-talking in the build-up, first saying Federer had to make it through to their meeting and then, once the match-up was established, that he was ready to send him packing.

Unfortunately for the 20-year-old, whose star is once again on the rise after a slump at the end of last year, there are few things the world No 2 likes more than to put these young whippersnappers in their place.

Tomic played outstanding tennis for the most part and looked likely to level the match at one set all when he led 5-2 in the second-set tie-break but Federer snatched it before running away with the third to claim another impressive victory in winning 6-4, 7-6, 6-1. In recent years, Federer has made a habit of looking every inch the likely champion with his performances in the first week, only to dip when he takes on the other top players, especially on hard courts.

He did, however, win his 17th Grand slam title at Wimbledon in the summer.

It will still take someone playing great tennis to beat him and the next one to try will be big-serving Milos Raonic of Canada.

"He's obviously got one of the best serves in the game," Federer said. "You always feel, especially after an off season like the one we've just had, he's maybe improved again on a few things or he's worked on a few things. So you would expect some more unexpected stuff that he didn't do last time around. We'll see how it goes. I'm excited about the match, anyhow."