Millie for .001 is the winner, imo.
May I propose 'milray' for .0001?
Mark Twain introduced a fictional elaboration of the mill in A Connecticut Yankee in King Arthur's Court. When Hank Morgan, the American time traveler, introduces decimal currency to Arthurian Britain, he has it denominated in cents, mills, and "milrays", or tenths of a mill (the name perhaps suggested by "myriad", meaning ten thousand or by the Portuguese and Brazilian milreis).
http://en.wikipedia.org/wiki/Mill_%28currency%29#Fiction12GHuMPPZDxDqtZZS6wP2FTv2c4V4KPohW