They say a gynecologist (or a protologist) is someone who would wallpaper the front hall of the house through the letterbox... and one has to say, remote control of a PC through a phone must come close to that...

Are these people mad? I can understand doing it over the Internet. But over Bluetooth? Shome mishtake, shurely...?

PalmOS has had it for over a year. http://www.free-press-release.com/news/200311/1068131901.html

I think Windows CE has it built in or something.

Neither of these clearly had compression beyond what Windows Terminal Services already does, but if there's a Web-based product that does the PC connection job, you can just point the Opera browser for smartphones at Opera's "Mobile Accelerator" service.