  We show that, contrary to a widespread belief, one can overcharge a near
extremal Reissner-Nordstrom black hole by throwing in a charged particle, as
long as the backreaction effects may be considered negligible. Furthermore, we
find that we can make the particle's classical radius, mass, and charge, as
well as the relative size of the backreaction terms arbitrarily small, by
adjusting the parameters corresponding to the particle appropriately. This
suggests that the question of cosmic censorship is still not wholly resolved
even in this simple scenario. We contrast this with attempting to overcharge a
black hole with a charged imploding shell, where we find that cosmic censorship
is upheld. We also briefly comment on a number of possible extensions.
