Nonlinear solutal convection in the melt under a planar solidifying surface is investigated in the limit of small segregation. Stationary solutions of the nonlinear problem are obtained and the preferred mode of convection is determined by a stability analysis. It is found that down‐hexagons (where motion is downward at the cells’ centers) are stable for sufficiently small amplitude &Egr;, while both down‐hexagons and squares are stable in a range of larger &Egr;. The dependence of various flow features on the segregation coefficient and the effective depth of the melt is discussed.