Enhanced layering is observed when molecularly thin films of a simple globular molecular fluid (octamethylcyclotetrasiloxane) are confined between step-free sheets of mica cleaved to be free of nanoparticulates produced by using a hot platinum wire. In addition, the linear shear responses depend on history. Films formed by rapid compression or under the action of shear display a large effective viscosity, but films formed by quasistatic compression display unprecedented low friction.