Using a large amount of aircraft measurements of cloud droplet size distributions, the relationship between cloud spectral relative dispersion ($varepsilon$) and cloud droplet number concentration (Nc) is studied. The results indicate that the value of $varepsilon$ varies between 0.2 to 0.8 when the cloud droplet number concentration is low (about 50 cm-3), and converges toward a narrow range of 0.4 to 0.5 when the cloud number concentration is higher. Because the distribution of the cloud droplet size is an important parameter in estimating the first indirect radiative effect of aerosols on the climate system, the uncertainty in the corresponding radiative forcing can be reduced by 10--40% (depending on cloud droplet number density) under high aerosol loading.. This finding is important for improving climate change projections, especially for the regions where aerosol loading is high and continues to increase.