The David Tennant Treat 4 Today is a video which I don't remember seeing before. It's not often I get to type that which is why this video has been chosen.
It's not great quality but it shows David Tennant being presented with some original concept artwork of a sonic screwdriver. His reaction at both the drawing and the packaging is sweet to watch.
The video was posted on 3rd June 2008 which was when David was already in rehearsals for Hamlet. As it was filmed in his Doctor Who trailer it must have been filmed sometime before June.