This paper develops a new approach for evaluating multi-step system forecasts when there are relatively few forecast error observations. In doing so, it combines Clements and Hendry (1993) with Abadir et al. (2014) to allow for estimation of the general forecast-error second-moment (GFESM) when there are more variables times horizons than forecast error observations. Simulations show that previous estimation methods deteriorate as observations decrease. The proposed approach compares well against alternative methods and provides correct forecast rankings even when there are relatively few forecast error observations.