Davydenko made it to the last four at Roland Garros last week
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Second seed Nikolay Davydenko made an early exit at the Gerry Weber Open as he went down 6-4 6-4 to Germany's Florian Mayer in round two.
World number three Davydenko has never won back-to-back matches on grass.
The Halle event also lost sixth seed Mikhail Youzhny to a back injury, to add to Roger Federer who withdrew on the eve of the tournament.
Marcos Baghdatis beat Robin Soderling 6-7 (7-9) 6-4 6-3, and Jarkko Nieminen beat Andrei Pavel 7-6 (7-5) 3-6 6-1.
Marc Gicquel of France defeated Germany's Benjamin Becker 6-2 7-6 (7-5) in the late match, while Youzhny's withdrawal gave Tomas Berdych a walkover.
"My coach says for these four weeks on grass, just take a holiday," said Davydenko after defeat by Mayer. "Otherwise I just get disappointed, frustrated.
"He didn't hit winners but after the ball was so low you have no chance to hit it back. What do you do?"
At the other end of the scale, Cypriot Baghdatis was bursting with confidence after his win and hopes to improve on last year's run to the Wimbledon semi-finals.
"For sure, this time I want to do better and win the title at Wimbledon - that's my goal," said Baghdatis.
"Now I play good on grass. I played on it a couple of times as a junior and was really bad."