With all-rounder Shane Watson ruled out through injury there was no place for second spinner Stuart MacGill, allowing batsman Michael Clarke to retain his spot when the two sides begin their next confrontation on Friday.
MacGill had hoped to be included at the batsman-friendly Adelaide Oval, but was again omitted from the squad as selectors retained their victorious line-up.
But chairman of selectors Andrew Hildtich said did not rule out picking two spinners later in the series.
"That decision is made more difficult while Shane Watson is unfit but it will be reviewed depending on the particular conditions we will face at each venue," he said.
Stuart Clark, the best bowler in the 277-run first Test win at Brisbane's the Gabba, seemed certain to retain his spot in the team ahead of fellow squad pacemen Mitchell Johnson and Shaun Tait.
Clark contributed impressive match figures of 7-93 and a quickfire 39 with the bat in the series opener.
But selectors retained Tait and Johnson as possible "options", with the team to be finalised later in the week.
Tait's ability to swing the ball and Johnson's variety, being a lefthander, are both appealing.
Both the 12th man and the other player to miss the starting XI will be released to play domestic cricket
Following his first innings 56 in the first Test, batsman Clarke is poised to retain his spot in the absence of all-rounder Watson, who has not recovered from the hamstring injury that kept him out of the Brisbane Test.
"We'll continue to look at our options to improve the team as we prepare for a series of tough Ashes encounters," Hildtich said.
"Michael Clarke seized his opportunity after being called in at late notice and played extremely well throughout the first Test and again this highlights the strength of Australian cricket."
The Squad: Ricky Ponting (captain), Adam Gilchrist (vice-captain, wk), Stuart Clark, Michael Clarke, Matthew Hayden, Mike Hussey, Mitchell Johnson, Justin Langer, Brett Lee, Damien Martyn, Glenn McGrath, Shaun Tait and Shane Warne.