The simulation of polymer flows is a complicated problem. One of the limiting factors is the degree to which elasticity plays an important role in the flow. For a given constitutive equation and numerical technique, a higher material relaxation time will result in a lower maximum deformation rate for which convergence is possible. Since industrial processes typically involve large deformation rates, a practical way to allow their simulation is to truncate the longest relaxation times. In this work the Leonov constitutive equation was used to simulate flow through an abrupt contraction. The possibility of truncating the relaxation spectrum was explored and the impact of using truncated spectra on simulations is described. Finally, we propose a technique for obtaining a truncated relaxation spectrum that will be useful for flow simulations.