If one tries to convert the circuit to 20A will run afoul of NEC article 250.122(B) because the equipment grounding conductor will be to small in a NM type cable. (6 & 8 AWG NM cable has a 10 AWG grounding conductor).
This is a copy & paste from the 2008 NEC. (Unchanged from 2005).
(B) Increased in Size. Where ungrounded conductors are
increased in size, equipment grounding conductors, where
installed, shall be increased in size proportionately according
to the circular mil area of the ungrounded conductors.
Bold by me.
If the cable is 3-conductor W/ ground a small subpanel would be the ticket.