Suppose a vector autoregressive moving-average (VARMA) model is estimated for m observed variables of primary interest for an application and n-m observed secondary variables to aid in the application. An application indicates the variables of primary interest but usually only broadly suggests secondary variables that may or may not be useful. Often, one has many potential secondary variables to choose from but is unsure which ones to include in or exclude from the application. The paper proposes a method called weighted-covariance factor decomposition (WCFD), comparable to Stock and Watson's (2002a,b) method here called principle-components factor decomposition (PCFD), for reducing the secondary variables to fewer factors in order to obtain a parsimonious estimated model that is more effective in an application. The WCFD method is illustrated in the paper by forecasting quarterly-observed U.S. real GDP at monthly intervals using monthly-observed 4 coincident and 8 leading indicators from the Conference Board (2018). The results show that root mean-squared errors of GDP forecasts of PCFD-factor models are 0.9%-11.3% higher than those of WCFD-factor models especially as estimation-forecasting periods pass from the pre-2007 Great Moderation through the 2007-2009 Great Recession to the 2009-2016 Slow Recovery.