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, <math><msub><mi>c</mi><mi>H</mi></msub></math>, is well defined and satisfies a two-sided bound. <math><msub><mi>c</mi><mi>H</mi></msub></math> 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 <math><mi>s</mi></math>, expressed as <math><mi>M</mi><mo>(</mo><msub><mi>H</mi><mi>i</mi></msub><msub><mi>H</mi><mi>i</mi></msub><mo>→</mo><msub><mi>H</mi><mi>j</mi></msub><msub><mi>H</mi><mi>j</mi></msub><mo>)</mo><mo>=</mo><msub><mi>c</mi><mi>H</mi></msub><mi>s</mi><mo>+</mo><mi>O</mi><mo>(</mo><msub><mi>g</mi><mi>SM</mi></msub><mo>,</mo><msup><mi>s</mi><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo>)</mo></math> where <math><msub><mi>g</mi><mi>SM</mi></msub></math> 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 <math><msub><mi>c</mi><mi>H</mi></msub></math> is equivalent to a bound on the dimension-six operator <math><msub><mi>O</mi><mi>H</mi></msub><mo>=</mo><mo>∂</mo><mo>|</mo><mi>H</mi><msup><mo>|</mo><mn>2</mn></msup><mo>∂</mo><mo>|</mo><mi>H</mi><msup><mo>|</mo><mn>2</mn></msup></math>.

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