Data from three cloudy days (3, 21, and 29 March 2000) of the Atmospheric Radiation Measurement (ARM) Enhanced Shortwave Experiment II (ARESE II) were analyzed and broadband absorptances were obtained for three sets of instruments. Grand (total flight) averages of fractional solar absorptances were ~0.21--0.22, with the exception of 3 March when two sets of instruments gave values smaller by ~0.03--0.04. The robustness of these values was evaluated by examining potential sampling problems with the aid of 500 nm spectral fluxes. The grand average of 500 nm apparent absorptance was statistically indistinguishable from zero for 21 and 29 March but acquired a large positive value of ~0.10 on 3 March, which is not physically understood. We present results showing that each of the three days is unique in terms of cloud morphology and behavior of the absorptance time series. When the conditional sampling method is applied to the two days with reliable 500 nm absorptances (21 and 29 March), the resulting histogram of broadband absorptances is significantly narrower than the histogram constructed from the original time series. Corrections to the absorptance time series ¿ la Cess et al. <1999> were successful for all three days because of the generally good correlation between broadband and 500 nm absorptances, removing the bulk of low-end and high-end extremes most likely associated with sampling and horizontal flux artifacts. The above two methods suggest an ARESE II range of broadband absorptances of ~0.18--0.26. Finally, our study shows that the data set obtained on 29 March is the most self-consistent and straightforward to analyze among the three, because this day fulfilled all the requirements of the ARESE II experimental design, namely the presence of thick, overcast, homogeneous clouds.