An s-channel model for inelastic reactions at high energies is presented. The scattering amplitude is split up into the contribution from the right-hand cut ( Tr.h.c.) and that from the left-hand cut ( Tl.h.c.) in a fixed- t dispersion relation; Tr.h.c. is assumed to be dominated by the peripheral s-channel resonances associated with a complex pole b0 ( s) in the impact-parameter plane. It yields the rotating-phase part of the amplitude; Tl.h.c. is assumed to be the analytic continuation of the analogous term in the u-channel. It provides a real, non-peripheral background in the s-channel. The predictions of this model for the t-dependence of high-energy amplitudes are confronted with experiment. A very good agreement is found in all cases. Moreover, we present an analytic expression for the complex pole trajectory b0 ( s), which agrees with the experimentally determined one and with analyticity requirements. This crucially interlocks the two terms Tr.h.c. (being a function of b0 ( s)) and Tl.h.c. (being a function of b0( u)).