Previous studies have documented multidecadal decreases in downward surface solar radiation (“solar dimming”) followed by increases in surface radiation (“solar brightening”) over Europe. A recent investigation reports that the radiation trends mainly occur under cloud-free skies and thus represent primarily the direct aerosol effect. We now compare cloud-free solar dimming and brightening trends in IPCC-AR4 20th century simulations with observed trends and examine how sulfate and black carbon aerosol histories, used as model input, affect these trends. Model output is obtained from all IPCC-AR4 models providing surface solar irradiance fluxes under cloud-free skies (14 models). Observational fluxes are derived from a combination of a) satellite cloud estimations, synoptic cloud reports, and surface solar irradiance measurements, and b) sun shine duration measurements and variability of the atmospheric transmittance derived from solar irradiance measurements. Most models display a transition from solar dimming to brightening, but the timing of the change varies by about 25 years. Hence, large discrepancies in sign and magnitude occur between modeled and observed dimming / brightening trends (up to 5.3 Wm^-2 per decade (dec) between models). The fact that fewer than half of the models consider black carbon aerosols explains part of the differences found between models as well as between models and observations. Considering all models with identical aerosol histories, differences in cloud-free radiation trends are less than 1 Wm^-2 dec^-1, except for one outlier with a difference of 2.7 Wm^-2 dec^-1. Thirteen of the fourteen models produce a transition from dimming to brightening that is consistent with the timing of the reversal from increasing to decreasing aerosol emissions in the input aerosol history. Consequently, the poor agreement between model and observed dimming and brightening is due to incorrect aerosol emission histories rather than other factors.