After heavy falls on Monday, the benchmark NZX50 index closed up 21 points, or 0.6%, to 3285.
In currency markets, the NZ dollar was at 82.35 US, 79.49 Australian, 51.95 pence, 63.48 yen, and 0.6023 euro. The TWI stood at 72.05.
Telecom was up 5 cents to $2.515 after releasing details of its plans to split. Mark Verbiest will succeed Wayne Boyd as Telecom's chairman if the demerger of the company goes ahead.
Fletcher Building rose 6 cents to $7.71, but Contact Energy fell 1 cent to $5.24.
Sky City Entertainment was up 5 cents to $3.45, Sky Network Television was up 3 cents to $5.39 and Auckland International Airport was up 4 cents to $2.29.
Fisher & Paykel Healthcare rose 3 cents to $2.15, while The Warehouse was up 1 cent to $3.44.
New Zealand Oil and Gas rose 1 cent to 72 cents after announcing on Monday that Pike River Mine's insurers agreed to an $80 million insurance settlement.
Goodman Property Trust was unchanged at $1, and Kiwi Income Property Trust was down 0.5 cents to $1.035.