New Zealand are "quietly optimistic" that Trent Boult and Colin de Grandhomme will be fit to play in Australia.
Boult and de Grandhomme missed the second Test against England after sustaining injuries during the victory in Mount Maunganui. And while New Zealand coach, Gary Stead, admits it is too early to know for sure if the pair will be available for the Perth Test on December 12, he described progress so far as "encouraging".
Both players will be obliged to step up their rehabilitation in the coming days. While they have had gentle bowls over the last couple of days, they will be pressed a little harder on Wednesday and then expected to deliver "a decent spell" on Friday. Only after that will a decision be taken on whether they fly to Perth on Saturday.
If either of them struggle to get through those sessions, Stead suggested a replacement would be called into the squad.
"Both Colin and Trent are progressing well, which is encouraging for us," Stead said. "Colin could have kept bowling through the last Test so he's probably just a little more advanced. But Trent actually rocked up really well today.
"Both have rolled their arm over at a very low level in the last two days. But both are going to have to prove their fitness a couple of days out from the first Test and bowl a decent spell of 10-12 overs at least over two or three spells.
"I don't know if I'm really confident, but I'm quietly optimistic they're tracking where we want them to be. But it's a long way to go if we know they're not going to play, so it's likely we'd look at replacements."
In an ideal world, New Zealand would probably have time to reflect on an excellent series victory over England - their fifth home series win in succession and their second over England in little more than 18 months - before heading into another Test campaign. But such are the schedules in modern international cricket that they will instead be obliged to go into a day-night Test in Perth without any sort of warm-up game. Instead, three training sessions - two of which are under lights - will have to suffice.
"It's just another thing to adapt to," captain Kane Williamson said phlegmatically. "Such is the international schedule. We fly out in a couple of days, have a bit of training and we're straight into another match. So it is quite a quick turnaround.
"The conditions - the surfaces - are quite different. They will bounce a bit more. This was a brilliant series win for us, but we're going to have to adapt quickly. We know it's tough - a lot of the guys have been there before - and we know they're very strong, clinical in their own [backyard]. We'll look forward to the challenge."
Williamson also confirmed that opener Jeet Raval, who endured a miserable series, would be retained for the Australia series. Raval made just 24 runs in the series falling to a couple of loose shots in his first two innings and failing to review a leg-before decision which replays show he hit in his third. His most recent seven Test innings have produced five single-figure scores - including two ducks - and a best of just 33.
But his long-term record is decent - he scored his maiden Test century only six Tests ago - and New Zealand have not lost faith in him at this stage.
"These things happen," Williamson said of Raval's grim series. "He has had a number of successful times at the top of the order with Tom Latham and he has been up against a really strong bowling attack here against England. He's been playing well and he's been very successful. He'll be turning his focus to Australia now."
A 213-run partnership between Williamson and Ross Taylor shepherded New Zealand to safety on the final day in Hamilton. Despite resuming with their side still in deficit, the pair both completed centuries - Williamson's 21st at Test level; Taylor's 19th - to ensure the draw. During the course of his innings, Taylor also became the second New Zealand batsman to make 7,000 Test runs (Stephen Fleming is the other) and passed 1,000 Test runs at Seddon Park. This was his sixth Test century at the ground in 12 Tests.
While Williamson admitted he had been fortunate to survive a remarkable dropped chance to Joe Denly - it really was as simple as they come at this level - such is his confidence at present, he hinted that he was a bit disappointed that the rain curtailed this Test denying New Zealand the chance to chase victory.
"It was a great effort form the guys after being slightly up against it after the first innings," he said. "A lot of hard work went into saving the match in the end when rain didn't allow us time to win it. But overall it was a really good effort. Ross' record here is incredible.
"The catch? It was fairly simply. No doubt Joe Denly is disappointed. The bowler, Jofra Archer, certainly was. I was very fortunate. You don't get many opportunities like that."