The feasibility of manipulating the single molecule absorption-emission cycle using picosecond stimulated emission depletion (STED) is investigated using a stochastic computer simulation. In the simulation the molecule is subjected to repeated excitation and depletion events using time delayed pairs of excitation (PUMP) and depletion (DUMP) pulses derived from a high repetition rate pulsed laser system. The model is used to demonstrate that a significant and even substantial reduction in the occurrence of 'dark states' in the fluorescence emission can be achieved using stimulated emission depletion. Variation in the PUMP-DUMP window allows precise control of the fluorescence yield with substantial increases in the fluorescence intensity observed at early PUMP-DUMP delays.