This paper proposes several procedures for testing the specification of an econometric model in the presence of one or more alternative models that purport to explain the same phenomenon. These procedures are closely related but not identical to the non-nested hypothesis tests proposed by Pesaran and Deaton, and they share similar asymptotic properties. The tests are conceptually and computationally simple, and they can be used to test against multiple alternative models simultaneously. The paper presents empirical results suggesting that these tests are effective at rejecting false hypotheses in practice. The paper introduces three tests: the J-test, the C-test, and the P-test. The J-test is used when the model is linear, the P-test when it is nonlinear, and the C-test as a preliminary test when the model is nonlinear and the derivative matrix is difficult to compute. The J-test involves estimating both α and β jointly, the C-test estimates α conditional on β, and the P-test is based on a linearization of the model. The paper also discusses the asymptotic properties of these tests, showing that they are asymptotically distributed as N(0,1) under the null hypothesis. The J-test and P-test are asymptotically perfectly correlated, and both are asymptotically negatively correlated with the CPD test statistic. The paper compares the power of these tests and the CPD test, finding that both tests reject the null hypothesis when the alternative hypothesis is true with probability approaching one as the sample size increases. Empirical results are presented, showing that the J-test, P-test, and CPD test reject the null hypothesis in most cases. The results suggest that the tests are effective at rejecting false hypotheses, even when testing against other false hypotheses. The paper concludes that these tests are simple to compute and can be used widely in applied econometric work.This paper proposes several procedures for testing the specification of an econometric model in the presence of one or more alternative models that purport to explain the same phenomenon. These procedures are closely related but not identical to the non-nested hypothesis tests proposed by Pesaran and Deaton, and they share similar asymptotic properties. The tests are conceptually and computationally simple, and they can be used to test against multiple alternative models simultaneously. The paper presents empirical results suggesting that these tests are effective at rejecting false hypotheses in practice. The paper introduces three tests: the J-test, the C-test, and the P-test. The J-test is used when the model is linear, the P-test when it is nonlinear, and the C-test as a preliminary test when the model is nonlinear and the derivative matrix is difficult to compute. The J-test involves estimating both α and β jointly, the C-test estimates α conditional on β, and the P-test is based on a linearization of the model. The paper also discusses the asymptotic properties of these tests, showing that they are asymptotically distributed as N(0,1) under the null hypothesis. The J-test and P-test are asymptotically perfectly correlated, and both are asymptotically negatively correlated with the CPD test statistic. The paper compares the power of these tests and the CPD test, finding that both tests reject the null hypothesis when the alternative hypothesis is true with probability approaching one as the sample size increases. Empirical results are presented, showing that the J-test, P-test, and CPD test reject the null hypothesis in most cases. The results suggest that the tests are effective at rejecting false hypotheses, even when testing against other false hypotheses. The paper concludes that these tests are simple to compute and can be used widely in applied econometric work.