His recent test form is modest - nine wickets at 64 apiece in his past six matches - but the draining effect of the first two tests in the ANZ international series means coach/selector Mike Hesson will need to think hard before sticking with the present trio.
Captain Brendon McCullum said on Monday that retaining the same XI for all three tests had merit and Hesson admitted it would be hard for a bowler to force his way in.
Bracewell joins the squad if all goes well in Christchurch. Ian Butler is there, too. It seems you can't have too many options.
"We need fresh bodies there in case guys don't scrub up," Hesson said. "It's been great they haven't had to bowl for the last three days [since last Friday, because of England enforcing the follow-on in Wellington] because our guys were hanging on by a thread for a while. I'd assume they'll be fine but we need to show a bit of due diligence there."
Bracewell needed "to get through 10 overs, and a good 10 overs".
So who makes way for Bracewell? If he gets a tick on arrival in Auckland, one of the left-armers Wagner or Boult. Four seamers are a possibility for Friday, but Hesson was speaking before seeing the pitch, and was giving spinner Bruce Martin - "he hasn't put a foot wrong" - a decent rap at the same time.
A demotion would be tough on the workhorse Wagner, whose 87 overs top the lot across the two teams so far, for nine wickets. Boult's four wickets have cost 39. Southee's solitary success came with his eighth ball of the series, but he'll be retained. They have toiled manfully, but sentimentality doesn't win tests.
Of England's pace trio only James Anderson has gone beyond 60 overs. Their bowling coach David Saker insists there is gas left in their collective tank and change is unlikely, fitness permitting.
Tall Steven Finn caused havoc on a bouncy Eden Park in the deciding ODI. He's managed just three wickets so far, but this is likely to be the venue most suited to his style.