Two design modifications to increase the evaporation/condensation and freshwater yield of conventional solar stills (CSS) are presented – absorber coating with black paint (BP) in which 10 wt % reduced graphene oxide (rGO) was dispersed, and use of a nano-silicon-coated glass cover alongside the rGO coated absorber. Water contact angle analysis revealed that the hydrophilic glass/condenser hindered water droplet movement, whereas the hydrophobic silicon-coated glass enabled significantly faster water droplet movement. The rGO-coated absorber SS, with 99.2% solar absorptivity, improved the average water temperature by 11% leading to an augmented full-day freshwater yield of 3031 mL (versus 2160 mL for the CSS). The synergistic effect of the nano-silicon-coated glass and rGO-coated absorber further enhanced the full-day freshwater yield to 3410 mL. Energy/exergy analysis demonstrated enhanced efficiencies of the combined condenser and absorber coated SS of 37% (energy) and 112% (exergy), compared to the CSS. Non-linear characteristic equations described the instantaneous gain in energy efficiency of the combined absorber and condenser coated SS. Absorber/basin exhibited the highest rate of irreversibility in all three SS. The cost of water was 0.01 $/L for the dual-modified still. Water physicochemical quality analysis before and after desalination revealed that the purified water was suitable for drinking. © 2022 Elsevier B.V.