Least-squares optimization of parameters generated by the Matrix Pencil Method usually improves fit quality. A speculative reason for this is that Matrix Pencil implementations involve Singular Value Decomposition, which minimizes squares of deviations in directions perpendicular to the solution vectors. Least-squares fitting, as usually implemented and as used here, minimizes squares of deviations perpendicular to the time axis. These differences in the measure of distance could lead to different optima. In any case, parameter value adjustments resulting from least-squares refinement are usually small. It is nevertheless worthwhile when precise characterization or comparison is needed. In this report, the autoregressive Matrix Pencil Method and component selection heuristics are used to determine the number of justifiable components, and to provide high-quality initial values for the parameters. Leastsquares refinement is routinely and reliably used to quickly find nearby local optima. The combined method is herein denoted ARM+LSQ.