A simple model is constructed to exploit the concept of drainage ''trees'' as observed during the process of expulsion for desalination of sea ice. Linear analysis is used together with a consistent approximation procedure for solution of the system to determine critical minimum Rayleigh numbers for the onset of instability. It is found that the system functions optimally when there is both a finite angle of tilt of the drainage channel as well as no tilt at all. The determination of the nonzero angle depends critically on the lateral mean density gradient, and numerical values for critical angles of inclination to the vertical obtained agree quantitatively with those reported.