This work shows the results of modeling and optimizing pentahedron-shaped covers for application on a passive solar still. While modeling under the assumption of clear weather in Provo, Utah, United States of America, it was found that two main geometries resulted: A single slope still with fully vertical back and sidewalls and a south face tilted at 37.1°, absorbing a total of 8.98 megajoules of direct solar radiation. A half-pyramid shaped cover with vertical backwall, sidewalls tilted in at 60.6°, and a south face tilted in at 41.5°, absorbing 9.34 megajoules of direct solar radiation.With improved covers, solar radiation absorbed by the basin can be maximized. Maximum radiation absorbed will generally indicate maximum still output.In addition, the internal convection of a passive solar still was modeled in order to compare with existing correlations to find the best convection correlation. The convection was modeled using Fluent 12 (CFD software package) and simulations were run for various geometries and temperatures. It was found that Shruti's correlation agreed the best with the CFD results. However, another possible correlation is suggested here which accommodates a higher range of Grashof numbers. For a correlation of the form Nu=C•(Ra)^n, it was found that C = 1.02, 0.56, and 0.66, and n = 0.19, 0.24, and 0.24 for cover tilt angles of 15°, 30°, and 45° respectively. Also, Grashof number ranges are 4.0 x 10^3 < Gr < 1.9 x 10^7, 4.0 x 10^4 < Gr < 1.9 x 10^8, and 2.1 x 10^5 < Gr < 1.0 x 10^9 respectively.