"Jimmy's had an injury-ravaged year, no doubt about that and when he managed to get back on the park for Otago it's fair to say his performances weren't consistently at a level either us or Jimmy would have wanted," Larsen said today.
"But what we've seen in the past is a genuine match-winning allrounder.
"The value of allround cricket is they're like gold dust. Corey and Jimmy are very important we believe to our future."
Their test numbers are similar, although Neesham's are slightly superior, whereas Anderson scrubs up better in short form cricket.
Neesham averages 38.25 in his nine tests, with two centuries, and has 12 wickets at 39 apiece.
Anderson, in 13 tests, averages 32.52, with one century, and has 16 wickets at 41.
When Anderson returned to action during the Sri Lankan visit last season, he spoke of his desire to keep playing as an allrounder. He wants to hold off any decision on giving up his useful left arm fast medium bowling as long as possible.
"Mike (coach and selector Mike Hesson) and I haven't had that discussion but it's obvious his back has been incrediblhy problematic," Larsen said.
"It's like Jimmy. The value of Corey to the team when he's operating at 100 percent with bat and ball is immense. We are all on the same page; we want him back on the park and in an allrounder capacity."
There are two newcomers to the list, Central Districts lefthander George Worker and Canterbury batsman Henry Nicholls, who had a taste of test action against Australia.
Worker did well in Zimbabwe and South Africa in white ball internationals early in the season; Nicholls was in the squad for the latter part of the summer.
Legspinner Ish Sodhi and bruising Auckland batsman Colin Munro make a return after missing out last season while the three players to drop off are the now retired brothers Brendon and Nathan McCullum, and short form allrounder Grant Elliott, who is only available for T20s this coming season.
The top-ranked player on the list - almost certainly captain Kane Williamson - will receive $205,266 as his basic salary for the year starting August 1.
Salaries drop in increments of about $7000, with players on a tiered system, dropping to the bottom player, who will receive $85,585.
On top of that, the match fees are $8495 per test; $3682 for an ODI appearance; and $2406 for each T20 match. New Zealand have 14 tests scheduled between August and the end of March next year.
The reason for the rise from 20 to 21 players is a variation in the Masters agreement between NZC, the New Zealand players' association and the six major associations.
The 21 New Zealand Cricket-contracted player for the 2016-17 year:
Corey Anderson, Trent Boult, Mitchell Santner, Ish Sodhi, Tim Southee, BJ Watling, Kane Williamson (all Northern Districts), Doug Bracewell, Adam Milne, Ross Taylor, George Worker (Central Districts), Mark Craig, Jimmy Neesham, Neil Wagner (Otago), Martin Guptill, Mitch McClenaghan, Colin Munro (Auckland), Matt Henry, Tom Latham, Henry Nicholls (Canterbury), Luke Ronchi (Wellington).
