What types of players would be wise for Cleveland to use its trade exception?

This may sound crazy but I would go with the person the longest possible contract. You don't want to get someone with 1 or 2 years left because I hate to be honest but Cleveland is not a hot spot for NBA players. They get someone with 1 or 2 years, they're going to be gone ASAP. I say get someone with 3 or more so that way at least you can have a star for a few years and hopefully Cleveland makes good draft choices, builds the team really strong and can convince the trade exception player to stay.