The classic cross-sectional regression (CSR) and mimicking portfolio (MIM) procedures estimate factor risk premia on a test asset span and the resulting tests of asset pricing models are performed with reduced degrees of freedom. Although we can restrict the risk premia of traded factors to equal expected returns, imposing such restrictions on nontraded factors is difficult, which may prevent full performance evaluation. We suggest testing with efficient MIMs that project factors onto a return space spanned by test assets and benchmark traded factors. The generalized method of moments (GMM) tests show that this approach generates more powerful tests and fair comparison against a benchmark model.