Cook has just two more chances to secure a first win of a troubled tour before flying home, when he will make a call on his leadership.
The 29-year-old has been backed by his team-mates to remain in charge, but victory in at least one, if not both, of the games that remain in the already-lost ODI series would provide a welcome relief.
Hanging over Cook's team also is the threat of levelling the worst run of defeats England has suffered, a sequence of 10 losses set in 2001 and 1993 - his side have now lost nine games in a row in all formats.
"We're trying to be really honest with ourselves," James Tredwell, the spinner, said. "We understand that we've not been good enough on this tour. We've spoken a lot about pushing back and giving Australia a bit of their medicine but that's not always easy when the skills aren't up to scratch. If we are honest about it that's been the issue this winter."
Australia will rest four of their key players, as David Warner, Brad Haddin, Shane Watson and Michael Clarke have not made the trip west.
Boyd Rankin is out for England with a hamstring problem, while Ben Stokes will be available despite missing Tuesday's session to attend a family funeral in New Zealand.