We critically assess to what extent it makes sense to bound the Wilson coefficients of dimension-six operators. In the context of Higgs physics, we establish that a closely related observable, $c_H$, is well defined and satisfies a two-sided bound. $c_H$ is derived from the low momentum expansion of the scattering amplitude, or the derivative of the amplitude at the origin with respect to the Mandelstam variable $s$, expressed as $M(H_i{H}_i\to H_j{H}_j)=c_{H}s+O(g_{\mathrm{SM}},s^{-2})$ where $g_{\mathrm{SM}}$ represents all Standard Model couplings. This observable is nondispersive and, as a result, not sign-definite. We also determine the conditions under which the bound on $c_H$ is equivalent to a bound on the dimension-six operator $O_H=\partial |H{|}^2\partial |H{|}^2$.