The supersaturation spectra of cloud condensation nuclei (CCN) are sometimes S-shaped and always asymptotically approach a limiting value as supersaturation becomes more than several percent. Such a complex shape can correspond to a bell-shaped size distribution of sub-micron aerosols. We found that an exponential expression N=N0(1-exp[-BSK>) fits measured supersaturation spectra better than the commonly used power law expression N=CSK, where N is the number concentration of CCN at the supersaturation S, N0 is the total number concentration of CCN, B, C and K are empirical coefficients. The exponential expression and the power law are related. For example, at S~0%, the exponential expression reduces to the power law, with C~N0B. The derived size distribution from the exponential expression agrees closely with measured size distributions for laboratory salts, but not for aerosols in polluted airmasses. The disagreement in polluted airmasses suggests that CCN have complex physiochemistry. ¿ 1998 American Geophysical Union