Originally Posted by Jim McDougall
Apparantly these are lighter, simple hilt swords that developed around the opening years of the 17th century that were in favor of the developing French school of fencing. The Italian and Spanish schools were much more conservative, and these were lighter, faster swords.
Because they were intended to be worn about town (as noted by Dmitry) they were essentially considered in a self defense type view, with the idea that as such they could easily be grasped from the bedside. There was apparantly a reference c.1655 to these type swords called 'walking swords', but the pillow thing seems to be an expression from about mid 18th century (Aylward, p.13).