Off-spinner Jeetan Patel has been added to the New Zealand squad for the second Test against Australia, starting in Adelaide next Friday.

Kyle Mills is to return home and will be available for Auckland's State Championship match, which begins on Monday.

Peter Fulton, who joined the team in Brisbane, will remain with the side and Gareth Hopkins will fly to Adelaide on Thursday to cover the wicket-keeping position.

Squad: Daniel Vettori (c), Grant Elliott, Daniel Flynn, Peter Fulton, Mark Gillespie, Gareth Hopkins, Jamie How, Chris Martin, Brendon McCullum, Iain O'Brien, Jeetan Patel, Aaron Redmond, Jesse Ryder, Tim Southee, Ross Taylor.