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The first meaningful effort of the game arrived in the 10th minute when Spurs summer signing Paulinho shimmied inside and curled goalwards, placing his shot too close to Michel Vorm in the Swansea goal.
Moments later Michu contrived to miss from just six yards out but had his blushes spared as the linesman's flag went up.
Midway through the half Spurs came within inches of going in front when Ashley Williams headed against the frame of his goal before Paulinho's snap shot was well held by Vorm.
Vorm was again tested in the 34th minute when Moussa Dembele let fly and saw his shot tipped over by the Dutch stopper.
The midfield duo of Dembele and Paulinho were the hosts' most threatening players and it was the latter who came close in the 39th minute when his controlled volley bobbled wide.