There's no expectation that the tourists will roll over again so lamely second time around.
"They're quality players and they're not going to make those mistakes in the second innings so we are going to have to be on top of our game," Southee added.
Southee said he hadn't personally been involved in the chat, but captain Kane Williamson and coach Mike Hesson will have crunched the numbers to see how New Zealand want to work through the next two days.
"We'll have a look tomorrow morning and come up with some plans."
The combination of England's feeble batting and New Zealand's controlled, thoughtful response, means a test which ordinarily would be battling by now to raise an eyebrow, let alone winning ambitions, still has plenty of juice in it.
New Zealand added four runs at the start of the day yesterday, enough to enable Henry Nicholls to complete his sixth test 50, before the rain arrived.
This test now has a minimum of 196 overs remaining - 98 overs per day, allowing for the 1.30pm start time, half an hour earlier than scheduled.
Here's one scenario: New Zealand press on and move their lead to about 250, which could be done by batting the first 90 minutes today, then declare and give themselves five sessions to bowl England out a second time and get any outstanding runs to win.
Sounds simple when you say it quickly, but England will have other ideas and you'd be daft to expect them to bat remotely as badly as they did first time around.
"The important thing is what happens in the rest of the game," batting coach and former England batsman Graham Thorpe said.
"You are playing for your country and get rocked over like that, your pride is dented but you can't feel sorry for yourself for long.
"You can just run for the hills or hide under the bed, you have to get up and go again the next day.
"You try and stay level with the players because they are going to feel bad enough.
"The rain has helped us a little bit, (we're) nowhere near out of the woods, but it's given them something to focus on."
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