It is shown, on the basis of potential theory, that for a Regge pole with position $\ensuremath{\alpha}(t)>\frac{1}{2}$ the reduced residue $\frac{\ensuremath{\beta}(t)}{{\ensuremath{\nu}}^{\ensuremath{\alpha}(t)}}$ behaves essentially as $[\frac{{\ensuremath{\alpha}}^{\ensuremath{'}}(t)}{R}]{R}^{2\ensuremath{\alpha}(t)}$ near threshold ($\ensuremath{\nu}\ensuremath{\lesssim}0$), where $R$ is the effective radius interaction. The quantity $\ensuremath{\gamma}(t)={(\frac{{{m}_{0}}^{2}}{\ensuremath{\nu}})}^{\ensuremath{\alpha}}\ensuremath{\beta}(t)$ which occurs in the asymptotic term $\ensuremath{\gamma}(t){(\frac{s}{2{{m}_{0}}^{2}})}^{\ensuremath{\alpha}}$ can therefore be considered as a slowly varying function of $t$ only if one takes ${m}_{0}={R}^{\ensuremath{-}1}$. Assuming that our threshold expression gives a qualitative description in the relativistic case, we note that if $\mathrm{Mr}>1$, where $M$ is the nucleon mass, then the normalization ${m}_{0}=M$ used in high-energy phenomenology will give rise to an exponential falloff of $\ensuremath{\gamma}(t)$ with ${(\mathrm{width})}^{\ensuremath{-}1}\ensuremath{\approx}2{\ensuremath{\alpha}}^{\ensuremath{'}}(0) \mathrm{ln} (\mathrm{MR})$. The values of $R$ in the $t$ channel of $\ensuremath{\pi}\ensuremath{\pi}$, $\ensuremath{\pi}N$, and $\mathrm{NN}$, estimated from the knowledge of the nearest left-hand branch points or factorization, occur in increasing order, and for each of them $\mathrm{MR}>1$. Our results for the Pomeranchuk trajectory roughly reproduce the exponential diffraction shape and indicate that a larger total cross section implies a sharper falloff of the amplitude in the diffraction region. A connection between ${f}^{0}$ and the diffraction width is discussed, as well as the question of zeros in $\frac{\ensuremath{\beta}}{{\ensuremath{\nu}}^{\ensuremath{\alpha}}}$.