A well-known folklore in combustion community is that curvature effect in general slows down flame propagation speeds because it smooths out wrinkled flames. As the first theoretical result in this direction, we prove that the effective flame speed is decreasing with respect to curvature diffusivity (Markstein number) for shear flows in the level-set G-equation model. The proof involves several novel and rather sophisticated inequalities arising from the nonlinear structure of the equation. We also show similar phenomenon in non-shear flows numerically. This is joint work with Jiancheng Lyu and Yifeng Yu.