In a Regge theory of spinless elastic scattering, subtraction constants in physical partial waves are not always free parameters. In a partial wave where there is no Castillejo-Dalitz-Dyson (CDD) pole, the subtraction constant $A_l\left(s_0\right)$, $s_0<4\mathrm{}{m}^2$, is uniquely determined when the left-cut term and the elasticity ${\eta }_l$ are specified. If there are CDD poles, all at finite points, then the subtraction constant is again fixed uniquely, but its value depends on the CDD parameters. If there is a CDD pole at infinity, the subtraction constant is unconstrained. These results are proved assuming that high-energy behavior is determined by a moving Pomeranchuk pole, with or without associated branch points. The analysis, although model independent, has implications for a dynamical model based on Reggeon exchange—namely, a model in which the input to the inelastic $\frac{N}{D}$ equation (left- and right-cut parts) is constructed from crossed-channel Regge terms. In such a model the $\frac{N}{D}$ equation is a regular Fredholm equation without high-energy truncation. In general, the phase shift obtained as output from the $\frac{N}{D}$ equation has the high-energy behavior required by Regge theory if, and only if, the subtraction-constant constraint is satisfied. It is argued that new calculations are needed to test the Reggeon-exchange model. Earlier calculations in the Chew-Jones scheme are not conclusive for the formulation given here.

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