Microsoft's lawyers have described themselves as "optimistic" that the European Union's antitrust hearings will deliver a positive outcome for the company, as the second day of the private meetings began. 

Speaking to the press gathered at the hearing today, Microsoft's top lawyer Brad Smith claimed that the first day's talks had been "constructive". 

"In fact I wish we could have had had this type of dialogue sooner," he said.

Microsoft could be forced to pay fines of €2m a day for not complying with the European Commission's demands that it open up its Windows operating system to competitors.

However, Smith felt that Microsoft had a good chance to make its case and avoid further fines.

"As we head into the second day, I am more optimistic that we will be able to resolve this issue," he said.