To price assets with a parsimonious set of factor-mimicking portfolios, one typically identifies and weights well-diversified basis portfolios. Traditional weightings lead to factor-mimicking portfolios that are unlikely to price even the basis portfolios from which they are formed. We offer a method to combine basis portfolios into a single factor-mimicking portfolio that is closely linked to the optimal portfolio. In practice, this method improves the pricing accuracy of parsimonious factor models, even for anomaly portfolios formed from characteristics that are distinct from those underlying the basis portfolios.