We investigate the reggeon cuts in a model with four-particle unitarity in the t -channel. The model, which was previously discussed by McCoy and Wu, is derived from ø 3 theory. Our analysis of asymptotic behaviour uses momentum-space techniques. We investigate carefully the integral equation for the partial-wave amplitude and use it to exhibit the origin of the various reggeon cuts, which turn out to satisfy discontinuity formulae consistent with Gribov's reggeon calculus. We suggest that there is a four-particle Regge pole to the right of all the cuts.