  Without any mechanism to protect its mass, the self-energy of the Higgs boson
diverges quadratically, leading to the hierarchy or fine-tuning problem. One
bottom-up solution is to postulate some yet-to-be-discovered symmetry which
forces the sum of the quadratic divergences to be zero, or almost negligible;
this is known as the Veltman condition. Even if one assumes the existence of
some new physics at a high scale, the fine-tuning problem is not eradicated,
although it is softer than what it would have been with a Planck scale momentum
cut-off. We study such divergences in an effective theory framework, and
construct the Veltman condition with dimension-six operators. We show that
there are two classes of diagrams, the one-loop and the two-loop ones, that
contribute to quadratic divergences, but the contribution of the latter is
suppressed by a loop factor of $1/16\pi^2$. There are only six dimension-six
operators that contribute to the one-loop category, and the Wilson coefficients
of these operators play an important role towards softening the fine-tuning
problem. We find the parameter space for the Wilson coefficients that satisfies
the extended Veltman condition, and also discuss why one need not bother about
the $d>6$ operators. The parameter space is consistent with the theoretical and
experimental bounds of the Wilson coefficients, and should act as a guide to
the model builders.
