The recently published hypothesis that the Cretaceous-Tertiary extinctions might be caused by an obstruction of sunlight is tested by model calculations. First we compute the total mass of stratospheric aerosols under normal atmospheric conditions for four different (measured) aerosol size distributions and vertical profiles. For comparison, the stratospheric dust masses after four volcanic eruptions are also evaluated. Detailed solar radiative transfer calculations are then performed for artificially increased aerosol amounts until the postulated darkness scenario is obtained. Thus we find that a total stratospheric aerosol mass between 1 and 4 times 10¹⁶ g is sufficient to reduce photosynthesis to 10⁻³ of normal. We also infer from this result that the impact of a 0.4- to 3-km-diameter asteroid or a close encounter with a Halley-size comet may deposit that amount of particulates into the stratosphere. The darkness scenario of Alvarez and others (1980) is thus shown to be a possible extinction mechanism, even with smaller size asteroids or comets than previously estimated.