Experimental measurements of the Critical Micelle Concentration (CMC) in diblock copolymer and molecular surfactant systems have shown a cross-over from the exponential decrease at short chain lengths to a much more shallow decay of the CMC when the solvophobic block length was increased. This effect was observed for a wide variety of surfactants, and has been attributed to the collapse of the solvophobic tail group. In order to study this peculiar effect in more detail, we performed grand canonical Monte Carlo simulations of model surfactants in combination with histogram reweighting to obtain the CMC as a function of solvophobic block length. We found that the CMC decreases exponentially with increasing solvophobic block length; no cross-over to a slower decay has been observed, as also expected based on theoretical considerations. These findings suggest that the experimentally measured CMCs may not be true equilibrium values, but that kinetic effects may be influencing the observed cross-over.