Steven Finn took 5 for 103 to enhance his hopes of starting next week's first Ashes test while England batsman Alastair Cook, Jonathan Trott and Kevin Piertsen pilled on the runs on day two of the final warm-up match against an Australia Invitational XI in Sydney.

The Middlesex seamer is competing for the final bowling place with Chris Tremlett and Boyd Rankin and did his hopes no harm with three wickets early on day two as the tourists knocked over their opponents for 304.

After a rain-hit warm-up game against Australia A, England's batsman were then handed significant time in the middle, but Michael Carberry, who had made a century in Hobart last week, made just 4 and fell in the sixth over to Josh Lalor.

But captain Cook (81) and Trott (83) put on 143 runs for the second wicket to reclaim control but when both departed, Pietersen, who came into the tour with concerns over a long-standing knee problem, struck 57 from 71 deliveries in typically brutal fashion.

Ian Bell made a sprightly 35 from 45 balls before Joe Root (26 not out) and Jonny Bairstow (11 not out) - standing in for the injured Matt Prior - steered England through to the close as they ended on 302 for 5.

"I thought the way we bowled this morning was fantastic and has put us in a good spot for this game," Trott said.

"The wickets here are conducive to the new ball so it's important as a batsman to get through that and then it becomes not as daunting as the new ball so it was god to get through that because I went in fairly early.

"I'm pretty pleased with my runs but I'm disappointed to get out the way I did. Hopefully tomorrow we can push on, the new ball is due in seven or six overs and we have a powerful tail coming into bat.

"We're not taking anything for granted because of the success we had here last time. The guys are really focused and very determined."