Solution-processed small-molecule p-DTS(FBTTh2)2:PC71BM bulk heterojunction (BHJ) solar cells with power conversion efficiency of 8.01% are demonstrated. The fill factor (FF) is sensitive to the thickness of a calcium layer between the BHJ layer and the Al cathode; for 20 nm Ca thickness, the FF is 73%, the highest value reported for an organic solar cell. The maximum external quantum efficiency exceeds 80%. After correcting for the total absorption in the cell through normal incidence reflectance measurements, the internal quantum efficiency approaches 100% in the spectral range of 600-650 nm and well over 80% across the entire spectral range from 400 to 700 nm. Analysis of the current-voltage (J-V) characteristics at various light intensities provides information on the different recombination mechanisms in the BHJ solar cells with different thicknesses of the Ca layer. Our analysis reveals that the J-V curves are dominated by first-order recombination from the short-circuit condition to the maximum power point and evolve to bimolecular recombination in the range of voltage from the maximum power point to the open-circuit condition in the optimized device with a Ca thickness of 20 nm. In addition, the normalized photocurrent density curves reveal that the charge collection probability remains high; about 90% of charges are collected even at the maximum power point. The dominance of bimolecular recombination only when approaching open circuit, the lack of Shockley-Read-Hall recombination at open circuit, and the high charge collection probability (97.6% at the short circuit and constant over wide range of applied voltage) lead to the high fill factor.