Penetration rates of an anthraquinoid acidic dye into the micelle of a cationic surfactant, hexadecyltrimethylammonium bromide (HTAB), were measured in the presence of potassium salts and 1-alcohols using the stopped-flow method. The rate constant, k, increases linearly with the increase in the concentration of added salt, and this accelerating effect varies with the nature of the added anion. This variation seems to arise from the difference in the counterion binding ability of the anion. The following two parameters regarding the anion are defined in this study; the acceleration ( a) as the increase in k with the increase in the concentration of added anion, and the relative counterion parameter (α) as the CMC depression effect of the anion relative to the bromide ion. Then, there is a linear relationship between these parameters. The alcohol addition also increases k, and its effect is in proportion to the carbon number of alcohol. However, based on the concept of the distribution of alcohol between the aqueous and the micellar phases, k was found to a function of the molar fraction of alcohol in the micellar phase ( Y a) independent of its carbon number. Therefore, it was suggested that the surface potential reduction of the micelle, which made the dye penetration smooth, was a main factor of the acceleration effect.