Through three-dimensional large-eddy simulations of marine stratocumulus we explore the factors that control the cloud spectral relative dispersion (ratio of cloud droplet spectral width to the mean radius of the distribution) as a function of aerosol number concentration and the extent to which the relative dispersion either enhances or mitigates the Twomey effect. We find that relative dispersion decreases with increasing aerosol number concentration (for aerosol number concentrations less than about 1000 cm-3) because smaller droplets resulting from higher aerosol number concentrations inhibit precipitation and lead to (1) less spectral broadening by suppressed collision and coalescence processes and (2) more spectral narrowing by droplet condensational growth at higher updraft velocity because reduced drizzle latent heating at cloud top results in increased boundary layer turbulent kinetic energy production by buoyancy and thereby stronger turbulence. Increased spectral broadening owing to increased cloud-top entrainment mixing, also as a result of increased boundary layer turbulence, is relatively insignificant compared with outcomes 1 and 2. The coefficient k, an important parameter that relates cloud droplet effective radius and volume mean radius in large-scale models, is a function of skewness and relative dispersion of the distribution and is negatively correlated with relative dispersion. Increasing k with increasing aerosol number concentration leads to maximum enhancement of the cloud susceptibility (the change of cloud optical depth due to change of cloud droplet number concentration) over that attributable to the Twomey effect alone by about 4.2% and 39% for simulated FIRE and ASTEX cases, respectively.