We present results on rare charm and B decays using 65 pb-1 of
data taken with the CDF detector in Run II.  Three results are discussed, a
measurement of the relative branching ratios Gamma(D0 ->
K+K-)/Gamma(D0 --> K pi) and Gamma(D0 --> pi+ pi-)/Gamma(D0 --> K pi)
and the direct CP-violating decay rate asymmetry, and a limit on the
branching ratio of the FCNC decay D0 --> mu+ mu-.  We also discuss the
prospects for the search for B0(s) --> mu+ mu- decays.