Several mechanisms have previously been proposed to explain differences between the shortwave reflectance of realistic cloud scenes computed using the 1D independent column approximation (ICA) and 3D solutions of the radiative transfer equation. When the sun is low in the sky, interception of sunlight by cloud sides tends to increase reflectance relative to ICA estimates that neglect this effect. When the sun is high, 3D radiative transfer tends to make clouds less reflective, which we argue is explained by the mechanism of “entrapment” whereby horizontal transport of radiation beneath a cloud layer increases the chances, relative to the ICA, of light being absorbed by cloud or the surface. It is especially important for multilayered cloud scenes. We describe modifications to the previously described Speedy Algorithm for Radiative Transfer through Cloud Sides (SPARTACUS) to represent different entrapment assumptions, and test their impact on 65 contrasting scenes from a cloud-resolving model. When entrapment is represented explicitly via a calculation of the mean horizontal distance traveled by reflected light, SPARTACUS predicts a mean “3D radiative effect” (the difference in top-of-atmosphere irradiances between 3D and ICA calculations) of 8.1 W m−2 for overhead sun. This is within 2% of broadband Monte Carlo calculations on the same scenes. The importance of entrapment is highlighted by the finding that the extreme assumptions in SPARTACUS of “zero entrapment” and “maximum entrapment” lead to corresponding mean 3D radiative effects of 1.7 and 19.6 W m−2, respectively.