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Both the computational costs and the accuracy of the invariant-imbedding T-matrix method escalate with increasing the truncation numberNat which the expansions of the electromagnetic fields in terms of vector spherical harmonics are truncated. Thus, it becomes important in calculation of the single-scattering optical properties to chooseNjust large enough to satisfy an appropriate convergence criterion; thisNwe call the optimal truncation number. We present a new convergence criterion that is based on the scattering phase function rather than on the scattering cross section. For a selection of homogeneous particles that have been used in previous single-scattering studies, we consider how the optimalNmay be related to the size parameter, the index of refraction, and particle shape. We investigate a functional form for this relation that generalizes previous formulae involving only size parameter, a form that shows some success in summarizing our computational results. Our results indicate clearly the sensitivity of optimal truncation number to the index of refraction, as well as the difficulty of cleanly separating this dependence from the dependence on particle shape.