England lose six wickets on final afternoon to fall to 251-run defeat
England had been 60-1 when Roy was bowled through the gate
Lyon takes six wickets and brings up 350 Test victims and Cummins, with four, passes 100 wickets
Australia's first victory at Edgbaston since 2001
Second Test begins at Lord's on 14 August
I'm a big fan of Sam Curran but how does he get into England's team? As a bowler who bats or as a batsman who bowls? He still hasn't scored a first-class century, for all of his good knocks down the order.
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Archer and Leach in for Jimmy (assuming injured) and Moeen. Maybe Curran for Denly as well as not really sure what he brings to the team. Better captaincy and coaching from the dressing room. The worry is that Starc is better than Siddle and the Aussies are confident now.
Jim, Bucks
A partnership of 39 between Moeen Ali and Chris Woakes - the vast majority of the runs scored by Woakes - held Australia up for a while in the afternoon session but once Moeen fell to Nathan Lyon again things finished quickly.
Stuart Broad went a ball later and a few overs afterwards Australia wrapped up victory...
The Australia players have been enjoying some time with their families at Edgbaston after wrapping up this famous win...
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Ollie: I think Sam Northeast deserves a go at number 4 as he has scored a lot of runs the last few years at Hampshire.
Dr Felix B Rowbotham OBE: Anyone calling for James Vince to come back has a very short memory. Let's have Keaton Jennings another shot too, shall we?
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Personally I'd look at ways to move Jason Roy down into the middle order. He's clearly got talent. Let him learn about Test cricket where his technique won't be as exposed by the new-ball swing.
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Mark: Surely Archer comes in for Anderson and I’d drop Mo who has lost all confidence with bat & ball with Leach coming in. Batting wise...you couldn’t argue if Denly or even Bairstow were dropped but I doubt England will panic. Sibley or Hain & Foakes could get in.
Mark Pearson: Sibley in for Roy, Leach in for Moeen, Archer in for Anderson & maybe Curran (or Stone if they want full pace) in for Broad. I'd also give the gloves to Buttler & tell Bairstow he only gets them back if he scores at least 150.
Leach will surely come in for the next Test. Moeen Ali really struggled in Birmingham. Leach was good with the bat last time out against Ireland. What about his spin? Will that be the answer?
Michael Vaughan
Ex-England captain on BBC Test Match Special
England will have to look at Jack Leach because Steve Smith averages 35 against left-arm spin versus pretty much 80 or 90 against every other form of bowling.
James Vince for a third go at Test cricket? He averages 24.90 from his 13 Tests so far. He did play a few decent knocks in Australia in the last Ashes series but is still yet to make an international hundred.
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It's simple: Vince in for Denly Leach in for Ali Archer in for Jimmy
Pete, in Surrey
It always looked a tall order at lunch, even with Jos Buttler and Ben Stokes at the crease. England were four down with two sessions left to bat.
Things got even worse when Buttler was out in the first over of the afternoon session.
Stokes and Jonny Bairstow hung around for a little while but then both fell in consecutive balls.
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There's a lot of love for Dom Sibley. He averages 39.3 in first-class cricket in 62 matches. He has 10 first-class centuries.
He has scored 940 runs at an average 62.67 this season in Division One with three hundreds.
Good enough?
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Leon Lewis: Roy, Burns, Root, Sibley, Stokes, Buttler, Foakes, Woakes, Archer, Broad, Leach.
Seb Waddington: Foakes for Bairstow, Sibley for Denly (Roy to 4), Leach for Moeen, and Archer for Anderson!
BBC Test Match Special
Australia batsman Steve Smith, speaking to Test Match Special: "It feels pretty special, winning the first Test in England is really special.
"It feels great, I'm loving being back playing cricket for Australia, doing what I love and contributing to wins. To score two hundreds in a match - the first time I've done that in any form of cricket in my life - is very special and I'm very proud.
"I didn't dream about how I would come back. I was jut letting time pass and when I got my elbow brace off after surgery something clicked and I was ready to play cricket again. I did lose that love for a little bit but I'm back doing what I love now and it's great.
"When I got that first hundred I was just thinking, 'Don't burst into tears.' That was as special as my first hundred back in 2013. It was a relief to get it out of the way.
"I copped a bit of stick out there but I'm not paying much attention to that and fortunately we've got a good Aussie contingent here. They're creating a good atmosphere for us and we're grateful for it."
You're not holding back.
What does everyone else think?
Bairstow, Denly, Moeen out. Foakes, Vince, Sibley and Archer in? Yes or no?
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SWgeezer74: Bairstow may as well be using the other end of the bat... Denly is not a test cricketer, Ali can't get the ball off the square and Buttler is batting too high.... Foakes, Vince, Sibley and Archer to come in.
But then Jason Roy was out in horrible fashion. He came charging down the wicket to Nathan Lyon. A shot for a Test opener? You decide.
That opened the door and England lost two more wickets before lunch - Joe Denly and captain Joe Root.