A NIH program director wrote one-page recom letter for my friend (just an usual A4 paper , no letterhead) and got 140 approved within 3 months, (another half year got 485 approved).
The first sentense this director wrote is: This reference is not authorized by official NIH or .., but based on my..."
The director did leave his office number and his title.
it is really a simple letter. But you know, it make a huge impact.