Impact of rotation on the convection parameter at marginal stability, χ_marg. We consider several azimuthal numbers with m > 3, for which SASI is stable in the absence of rotation. The m = 1 and m = 2 are not shown because they are unstable to SASI, which prevents us from measuring χ_marg. The curves are cut when the mode is unstable for all convection parameters, in which case χ_marg does not exist anymore.