Jonathan Stephens, permanent secretary at the DCMS, said Mr Smith was considered before the emails emerged to be someone who "understood and would abide by his proper role".
He told the inquiry the better the special adviser, the more reliable a guide they were to a Secretary of State's view.
"I think he was well tuned in to the Secretary of State's thinking," he said.
He went on:
The first suggestion that contacts went beyond what was proper was April 24 with the release of emails from Fred Michel and this was the first occasion I recall mention of Michel by name.
The following morning I told the Secretary of State I thought the number, extent, depth and tone of contacts supported by those emails went beyond what was acceptable.
Documents released by the Leveson Inquiry reveal the extent of News Corp lobbyist Fred Michel's contacts with senior figures in Government.
Adam Smith tells the Leveson Inquiry about his resignation after James Murdoch gave his evidence.
So it will be a big week at Leveson next week. Jeremy Hunt will finally get the chance to put his side of the story.