South Australia 7 for 222 (Head 109) trail New South Wales 289 (Solway 133*, Nevill 53, Sayers 8-64)
With the decision looming on Australia's Test batting line-up, Travis Head made a timely century against a strong New South Wales attack to shore up South Australia's first innings at Adelaide Oval although the visitors ended the second day with the advantage.
Head, who was left out of the final Ashes Test when Australia rebalanced their side with Mitchell Marsh, had made an unconvincing start to the first-class season with a scratchy half-century on a flat pitch at Junction Oval before scores of 0 and 12 against Queensland.
However, he was named in the Australia A side to face Pakistan in Perth later this month in what is billed as a showdown for probably two batting spots with Head vying for a middle-order role. He will now enter that game with confidence having brought up his 11th first-class hundred from 200 deliveries with a boundary off Australia team-mate Josh Hazlewood, but he could not reach the close as Hazlewood hit back during an impressive spell with the second new ball.
There was less from the rest of the batting order than he would have liked. Trent Copeland struck early to trap Jake Weatherald lbw although the batsman indicated he got an inside edge and Callum Ferguson edged to gully. Copeland struck again when a Henry Hunt got into a tangle against a short ball to leave South Australia 3 for 68.
Tom Cooper helped Head added 73 for the fourth wicket only to send a top edge to fine leg where Hazlewood took a well-judged catch. Another 50-run partnership followed before Nathan Lyon earned reward for a probing spell by having Harry Nielsen caught at slip, the batsman happy to take the word of Copeland that the ball had carried.
When Tom Andrews was caught behind off Moises Henriques shortly before the second new ball New South Wales were firmly on top and the removal of Head left them sensing a handy lead.
The day had started with New South Wales seven down in their first innings and Chadd Sayers claimed two of the remaining wickets to finish with a career-best 8 for 64. Debutant Daniel Solway, who marked the opening day with a century, finished unbeaten on 133.