Poyet is delighted to have the 25-year-old at his disposal.
The Uruguayan said: "I am sure we are going to make Lee a much better player than what people think, and that tells you how important he is for the football club.
"He is paying attention, he is always asking questions, he is always learning and if someone needed to play in this game above any game, it was Lee Cattermole, so there was no doubt in my mind about who was starting in the middle.
"Then, of course, you have got options, but I am sure he is going to be much better, and I hope he is going to keep helping us."
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