A dispersion relation has been derived which shows the combined stabilizing effects of convective damping (outgoing boundary condition), average curvature and finite Larmor radius (FLR) on ballooning modes. It has been found that, in contrast to the MHD case, the convective damping influences the stability threshold when FLR effects are included. The highest allowed shear as a function of mode number for free passage to the second stability region has been calculated analytically.