Rigorous lower bounds on the imaginary part of helicity-nonflip elastic amplitudes are derived under the assumption that their impact-parameter representations are monotonically decreasing functions of $b$ (central profiles). One result of these bounds is that at intermediate to high energies, typical Pomeranchukon-dominated elastic helicity-nonflip amplitudes must not have zeros for $\mathrm{}\left|t\right|\mathrm{}\lesssim 0.6$ Be${\mathrm{V}}^2$. A connection between the phenomenological absence of zeros in these Pomeranchukon amplitudes at small $\mathrm{}\left|t\right|\mathrm{}$ and the conjectured central behavior of the profile is thus established.

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