Asymptotic analytical solutions are derived for the configuration posed by Quon [Phys. Fluids 26, 632 (1983)] for diffusion-driven flow in a tilted square container when the diffusive parameter R is small. The key regions of the asymptotic structure are outlined and the leading-order solutions are determined in most of those regions. The analysis follows that in Page and Johnson [J. Fluid Mech. 629, 299 (2009)] and Page [Q. J. Mech. Appl. Math. (in press)] but includes an additional a??R1/4-layera?? region. Analytical solutions are compared with numerical results for small R and display excellent agreement. It is also shown that the solutions and flow structure are applicable over a wide range of Prandtl numbers.