Dual four-point functions with no negative residues

The positivity of residues in a general class of dual four-point functions is studied. A large domain in parameter space [$\alpha \mathrm{}\left(0\right)\mathrm{}$, ${\alpha }^{\prime }\mathrm{}\left(0\right)\mathrm{}$, trajectory curvature, external mass] is found in which there are no negative residues at any level. The ghost-free domain of $\alpha \mathrm{}\left(0\right)\mathrm{}$ expands as the positive curvature of the trajectory is increased. This suggests departure from linearity of trajectory as a way of breaking the $\alpha \mathrm{}\left(0\right)=1\mathrm{}$ no-ghost condition for the Veneziano $N$-point function. For a set of parameters which provides a good fit to the nondiffractive component of proton-proton elastic scattering, it is shown that the amplitude has no negative residues.