Using a novel two-step fabrication scheme, we create highly semiconducting-enriched single-walled carbon nanotube (sSWNT) bulk heterojunctions (BHJs) by first creating highly porous interconnected sSWNT aerogels (sSWNT-AEROs), followed by back-filling the pores with [6,6]-phenyl-C-71-butyric acid methyl ester (PC71BM). We demonstrate sSWNT-AERO structures with density as low as 2.5 mg cm(-3), porosity as high as 99.8%, and diameter of sSWNT fibers <= 10 nm. Upon spin coating with PC71BM, the resulting sSWNT-AERO-PC71BM nanocomposites exhibit highly quenched sSWNT photoluminescence, which is attributed to the large interfacial area between the sSWNT and PC71BM phases, and an appropriate sSWNT fiber diameter that matches the inter-sSWNT exciton migration length. Employing the sSWNT-AERO-PC71BM BHJ structure, we report optimized solar cells with a power conversion efficiency of 1.7%, which is exceptional among polymer-like solar cells in which sSWNTs are designed to replace either the polymer or fullerene component. A fairly balanced photocurrent is achieved with 36% peak external quantum efficiency (EQE) in the visible and 19% peak EQE in the near-infrared where sSWNTs serve as electron donors and photoabsorbers. Our results prove the effectiveness of this new method in controlling the sSWNT morphology in BHJ structures, suggesting a promising route towards highly efficient sSWNT photoabsorbing solar cells.