But if they back Southee, New Zealand will surely do so with fingers crossed and aware of the need to be sure they have sufficient fast-medium cover in case of a relapse.
Left armers Neil Wagner and Mitchell McClenaghan will be in the thinking, but Matt Henry may have first dibs.
That could have New Zealand fielding four seamers, Mark Craig - on the back of a ringing endorsement from his captain today - batting at No 7, and a worryingly long tail.
Playing BJ Watling as a specialist batsman and bringing in Luke Ronchi to keep would help the batting, but would leave just four specialist bowlers. That could be dicing with disaster if Australia's batsmen get away as they did on day one at the Gabba.
New Zealand do have form for bouncing back effectively after losing opening tests of series recently, notably in the United Arab Emirates and England within the past year.
But the WACA ground and the opponents, with their tails up, make this a vastly harder proposition.
Among the curious moments in the first test was New Zealand players' propensity for rushing up to departing Australian centurymakers to congratulate them as they left the field.
It tallies with New Zealand's good guy image, and gets a mocking from Australian media, and even some of their players.
David Warner remarked before the first test that Australia weren't in the game to win spirit of cricket awards.
Australian media found the handshaking either bemusing or plain dopey, especially when Warner and opener Joe Burns had scored the softest hundreds they'll ever get against seriously ordinary New Zealand bowling in the second innings.
The impression is New Zealand could do with taking some harden-up pills.
Sure, it may go against the often-stated philosophy of how McCullum's team want to play their cricket. But the corollary is that one team looks determinedly ruthless, the other not pushing back as hard as they might.
That, however, is a side issue to the main problem for New Zealand, which is finding ways to, at the very least, make life harder for Australia's batsmen.
There are permutations to consider. New Zealand must get their choices right for the sake of the series. There's no wriggle room left.