Help! My window blinds are a mess!

I have very expensive honeycomb blinds that are a tragic, filthy mess. They are a very light color, although after all the NYC filth has gotten them to them, they are about 4 shades darker. Does anyone know of a remedy to help clean these? I'm afraid to take them down and wash them in soap in the tub, because I don't want to set the filth in deeper. Is there a special cleaner that I should use? I would appreciate any advice here.