Analytic and numerical studies of prescriptions for T-matrix averaging are presented in the context of a coupled-channel model with separable potentials. The inelastic channels are folded into an optical potential and the corresponding branch cuts are discretised by expanding in R-matrix and in L² bases. This singular optical potential leads to irregular structure (pseudoresonances) in the T-matrix element for elastic scattering, whose explicit form is known due to the analytic solubility of the model. Two procedures for extracting the physical T matrix are discussed: averaging of the irregular T matrix over an infinitesimal interval and the frequently used method of a least-squares fit for a finite interval. Analytic proofs of the convergence of these averages to the exact T matrix are given and the convergence rate is investigated.