Having stared down England, the chants of the Hollies Stand and their own doubts, the Australian side led by Tim Paine has still more improvement in it, the captain has claimed, not least the tourists' most dominant forces of Edgbaston, Steven Smith and Nathan Lyon.

Smith won the match award for a spine-tingling double of 144 and 142 in his first match back from the Newlands scandal ban, leaving Paine to marvel at his concentration while also admitting his tactical alertness had been of major assistance throughout the Test. However, Paine's most telling remark about Smith and Lyon, who spun England out with a startling 6 for 49 on the final day that also took him past 350 Test wickets, was that both have shown the ability to keep building on their games as senior players.

"He could get plenty. As long as he wants to go for I reckon, he doesn't seem to have too many niggles or injuries over his career," Paine said when asked how many more wickets Lyon might take. "The ball is coming out as well as ever. He's a bit the same as Smithy, I feel like every Test match or series they seem to get better which is astonishing at their age. But I think if you come and watch both of them train you see why they keep improving and keep getting better and are a great example for the rest of our group.

"No doubt the pitch had worn but I thought he was threatening in the first innings as well. Nathan has played on all different surfaces now and knows exactly what he is doing in all different situations. I think he bowled a bit quicker, which he tends to do over here because he doesn't get the bounce he gets in Australia or the turn as consistently. He controlled it beautifully and he is going to be a real threat. He can take day five wickets and when you have a spinner like that it can change a game very quickly."

After bearing so much of the leadership load over the past year, Paine said he had gained a lot from the ability to delegate in this match, even if there were times when it looked as though Smith was controlling proceedings almost as much as the official captain was, while David Warner also had input. "It certainly helps. Both of those guys in particular have played a lot more cricket in England than I have," Paine said. "They've played a lot more big tournaments and big series and big Tests than I have.

"The same goes for all of our team - they're not only helping me with the way they lead our group, they're also helping ... the things that Marnus Labuschagne, Mitch Marsh and Travis Head are learning from Steve Smith and Daivd Warner in our change room is stuff that cannot be taught. We're all tapping into them whether we're the captain, the coach, the batting coach or bowling coach. They've got things they've learned through experience that other people don't have or don't know. Like I said before, we'd be foolish not to tap into that. They've still got a huge presence in our dressing room, there's no denying that."

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With a tour game in Worcester beginning on Wednesday, the Australians will look to rest key players, notably the bowlers in this Test and also Smith. Nevertheless, Paine said he would not be standing in the way of allowing Smith to hit another surfeit of balls before the Lord's Test after the way his exhaustive preparation for Birmingham played out in the middle.

"I wouldn't argue with his preparation, it seems to work for him, but there's probably a few guys that will miss next week," Paine said. "We've got some guys who haven't played any cricket and some who have played through a World Cup and then straight into a tour game in Southampton and then into a Test match. So we've got to manage not just our fast bowlers but we've got to manage the guys who've been involved in the World Cup and we'll have that conversation today or tonight and make sensible calls."

Another key Australian performer to improve across the Test was Pat Cummins, who bowled presentably in the first innings but delivered truly fiery stuff in the second, starting with a sharp lifter to dismiss Rory Burns that drew life from a pitch that had seemingly breathed its last. "I think he said he just struggled in the first innings for a little bit of rhythm, which can happen, he hasn't played a hell of a lot with the red ball in the last six months, so I think there was a little bit of rhythm," Paine said.

"It was also a big series and something he wanted to have a real impact on so I think there was probably a little bit of nerves as well which was totally fine. I don't think he was on his own there, but I think he settled into the Test match beautifully and the way he set the tone for our team this morning was exactly what we want from Pat Cummins. Now he's settled into some rhythm I think he'll just get better and better.

"One of the reasons we pick so many bowlers was because we knew this Ashes series was going to be wearing on our bowlers. Especially the guys who were at the World Cup. We've got two world class bowlers sat on the sidelines raring to go [Mitchell Starc and Josh Hazlewood]. I imagine they'll bowl in the tour game and then put their hand up for selection. We'll look at the pitch when we get to Lord's and then make our selections on what will be the best combination to get us 20 wickets. We think we have a lot of different options."

Paine also disagreed that the selectors needed to feel "vindicated" by the performances of Matthew Wade and Peter Siddle, pointing out that both had been good, logical selections tailored to the conditions and also out of deference for their recent performances in first-class ranks. "Matty has been the form players in Australian cricket for the last 12 months. Siddle is someone we see as a handful in these conditions," Paine said.

"Even today on a day five wicket he took no wickets but he was still a handful. He asks questions all the time and with the Dukes ball in English conditions he is a real handful. He bowls a beautiful length over here. I wouldn't say they are punts, they were good, educated decisions from our selectors."