Mercedes driver Michael Schumacher beat McLaren's Lewis Hamilton to set the fastest time in practice at the Chinese Grand Prix.
Schumacher was 0.172 seconds ahead of Hamilton, who was on course to beat the German until he lost time in the final sector of his fastest lap.
The Red Bulls of Sebastian Vettel and Mark Webber were third and fourth, ahead of Mercedes' Nico Rosberg.
The second session was dry after rain affected the first in the morning.
Schumacher's pace-setting performance came a day after race stewards declared a controversial design feature on the Mercedes legal, following a protest from Lotus.
Many believe the design, which boosts the DRS overtaking aid and enhances straight-line speed, will put Mercedes in the fight for pole position on this track, which has one of the longest straights on the calendar.
However, BBC F1 technical analyst Gary Anderson said Mercedes were still struggling with higher tyre wear in race trim than their main rivals.
Hamilton, who has been on pole for both races so far this season, was on a lap that was faster than Schumacher's but lost time in the final sector.
Button, though, was struggling in comparison, complaining of "way too much understeer" - a lack of front-end grip - on the radio to his engineers.
"It's been a difficult day for me trying to find a good set up," said Button. "My tyres have been up and down all over the place.
"It's very cold here, so it's difficult to get them hot enough. When you go through Turn 1, you damage the tyre a lot because the tyre is not in its working range - and then you lose a lot of rubber.
"Then it spirals out of control because the less rubber you have, the less heat you can generate so it gets worse and worse and worse."
Hamilton was fastest in the first session, which started on a damp track after overnight rain, and was further hit by a shower part-way through the session.
The 2008 world champion said on Thursday that he would have to take a five-place grid penalty because his gearbox needed changing.
"I do have to change my gearbox, unfortunately I need to take a new one. It doesn't faze me, it is what it is, we're just going to work on being as quick as we can in qualifying.
"During the race here you can overtake - we have a quick car so we can do that."
Vettel has a revised exhaust configuration on his car as Red Bull struggle to recapture the form that made the German world champion for the last two years.
The new design brings the exhausts back towards the centre and front of the car, in a similar position to where they were when the car first ran in pre-season testing.
According to Anderson, the idea is to make better use of the influential 'coke-bottle' area at the rear of the car.
The exhaust positioning on Webber's car, which is further back and away from the centre, is aimed at improving the airflow in the area between the rear wheels and floor - an approach taken by most other teams.
Vettel said his initial impressions were that he preferred the car in its new specification.
"Driving it I think I felt a bit more comfortable today, a bit more together," Vettel said, although he added that the team would have to analyse the data before deciding whether to stick with it.
Behind the McLaren, Mercedes and Red Bulls, Sauber's Kamui Kobayashi was seventh, ahead of the Force India pair Paul di Resta and Nico Hulkenberg.
Ferrari's world championship leader Fernando Alonso was only 10th fastest - 1.343 seconds off the pace.
BBC 5 live analyst Jaime Alguersuari said: "I think Ferrari are going to struggle here even more than they did in Australia and Malaysia. Their top speed is poor - and the long straight is a big influence on lap time here."
The difficult season of Alonso's team-mate Felipe Massa continued - he was nearly a second slower than the Spaniard, whose prediction that he will again be struggling to make it into the top-10 shoot-out in qualifying looks correct so far.
Another team having problems were Lotus, with Kimi Raikkonen 13th and Romain Grosjean 15th.
The team abandoned plans to do the usual race-simulation runs in the second session to spend more time trying to solve problems with the car.