In the present work, an effort is carried out to enhance the distillate yield of a single-slope basin-type solar still by increasing the heat input through its transparent walls and providing hanging wicks to increase the evaporation–condensation rates. A modified basin-type single-slope multi-wick solar still (MBSSMWSS) was proposed and fabricated to increase the productivity and improve the low efficiency of the recently designed modified basin-type single-slope solar still (MBSSSS). Experiments were conducted on both the solar stills to assess their performance, productivity, and efficiency (thermal and exergy) for the same basin area and water depth for the climatic condition of Prayagraj, Uttar Pradesh (U.P.), India. Results showed that the productivity, overall energy (thermal) efficiency, and maximum values of measured instantaneous exergy efficiency of the MBSSSS and MBSSMWSS systems were found to be 3.2 l/m2 day and 4.22 l/m2 day, 18.16% and 26.89%, and 4.28% and 5.31%, respectively. Furthermore, thermal modeling was also done using the energy balance equations, and then, a theoretical analysis was carried out to validate with the respective experimental observations. A good agreement was found between experimental and theoretical results. Finally, based on the results of the evaluation parameters and comparative analysis, the modified solar still with wick was found to be a better system compared with that of the system without wick and might be a good option as a solar desalination system.