"Every area needs improving," New Zealand captain Stephen Fleming said reflecting on a first match in which neither side exceeded 275 in an innings.
In that game the honours swung virtually every session, before New Zealand eventually won by 27 runs.
New Zealand need to win in Wellington to wrap up the three-match series and the West Indies must win to keep it alive, and Fleming believes he has the inside running.
"It's a lot easier when you're 1-0 up with a Test win. You can dissect areas that weren't special and move forward in a positive vein instead of trying to worry about the fallout of a Test loss," he said on Thursday.
"In the leadership group meeting we addressed a lot of those areas, but now it's up to individuals to prove they have made the changes."
The West Indies boast a formidable batting line up with Brian Lara, Shivnarine Chanderpaul, Chris Gayle, Dwayne Bravo and Daren Ganga but they need more of them to fire at the same time.
The 148-run opening partnership by Gayle and Bravo in the second innings of the first Test potentially put the West Indies in a winning position, but Lara's second consecutive first ball dismissal seemed to be the catalyst for the rest of the line-up to fold as well.
But despite the psychological damage from such a collapse, and having lost their past seven Tests, coach Bennett King put on a brave face to say his side is moving in the right direction.
"Sometimes you've got to get to the depths of despair before you start re-emerging," he said.
"Over the time that I've been here, I certainly think we've improved and progressed in different areas. We're creating opportunities to win Test matches."
Both sides face selection problems because of injuries, with the West Indies perhaps worst hit after injuries ruled Ramnaresh Sarwan and Jerome Taylor while allrounder Bravo has been unable to bowl since straining muscles in his left side in the opening match of the tour.
Sarwan's place in Wellington is almost certain to go to Runako Morton, whose 110 in the last one-day international is the only century so far by a West Indies batsman on this tour, while Daren Powell would come in for Taylor.
Kyle Mills has been drafted into the New Zealand squad as cover for the pace attack of Shane Bond, Chris Martin and James Franklin, who were all suffering niggles after the first Test.
All three were expected to get a clean bill of health for the Test on a Basin Reserve wicket which tends to seam on the first day.
This may give Mills the nod over Martin, who toiled for three wickets in the first Test in Auckland with a tendancy to bowl short.
Franklin was even more expensive but has the advantage of being a much stronger batsman at the bottom of the order.
With injuries forcing changes in the opposition, Fleming said he was loath to make too many changes as New Zealand looked to bed down a stable team.
"Even though some guys may not have picked up wickets and been below par, they should improve as the Test series goes on and too often we've probably chopped and changed and brought new players in," he said.
New Zealand (from): Jamie How, Hamish Marshall, Peter Fulton, Stephen Fleming (captain), Nathan Astle, Scott Styris, Brendon McCullum, James Franklin, Daniel Vettori, Kyle Mills, Jeetan Patel Shane Bond, Chris Martin.
West Indies (from): Daren Ganga, Chris Gayle, Runako Morton, Brian Lara, Shivnarine Chanderpaul (captain), Dwayne Bravo, Dwayne Smith, Denesh Ramdin, Daren Powell, Ian Bradshaw, Rawl Lewis, Fidel Edwards, Jerome Taylor.
Umpires: Mark Benson (ENG), Daryl Harper (AUS).