We show that single DiIC(12) molecules adsorbed on a silica surface display a new type of rapid intensity fluctuations between an "on" level and a "dim" level distinct from "on"-"off" blinking. These fluctuations are correlated in time and exhibit two correlation times, one of the order of 10 ms and the other of the order of 100 ms, which are likely due to small motions of the nuclear coordinates of the adsorbed molecule. In addition, molecules that show these fast fluctuations also have emission spectra blue-shifted from the emission spectrum of the ensemble, indicating that this behavior is sensitive to the binding site of the molecule.