Shallow trade cumuli over subtropical oceans are a persistent source of uncertainty in climate projections. Mesoscale organization of trade cumulus clouds has been shown to influence their cloud radiative effect (CRE) through cloud cover. We investigate whether organization can explain CRE variability independently of cloud-cover variability. By analyzing satellite observations and high-resolution simulations, we show that more clustered cloud fields feature geometrically thicker clouds with larger domain-averaged liquid water paths, smaller cloud droplets, and consequently larger cloud optical depths. The relationships between these variables are shaped by the mixture of deep cloud cores and shallower interstitial clouds or anvils that characterize cloud organization. Eliminating cloud-cover effects, more clustered clouds reflect up to 20 W/m2 more instantaneous shortwave radiation back to space.