New Zealand insist injured spearhead Trent Boult and all-rounder Colin de Grandhomme remain in the selection frame for this week's first Test in a series the tourists have vowed to remain disciplined and composed.

Boult (side strain) and de Grandhomme (abdominal tear) arrived with their teammates in Perth on Saturday but face an anxious build-up to Thursday for they each must pass a fitness test to take part in the inaugural day-night Test at Perth Stadium.

The pair missed the second Test against England last week but bowled and completed a light fielding session on Friday and are "progressing nicely", according to Black Caps bowling coach Shane Jurgensen. However, whether that prognosis is just to keep the Australians guessing is another matter, and one that will become clearer when the two squads train on Monday.

On song: New Zealand's innings defeat of England in the first Test proved they'll be worthy opponents in Perth. Credit:Getty

"They are both going quite well. Intensity wise at training [on Friday], they were pretty similar. I think they are both going quite well," Jurgensen said.