Summary: We consider \(m\) independent one-parameter exponential families with parameters \((\theta_ 1,\theta_ 2,\ldots,\theta_ m)\), and the alternative hypothesis \(H_ 1 :\theta_ i> \theta^ 0_ i\), \(i=1,2,\ldots,m\), where \(\theta_ i^ 0\)’s are specified. The null hypothesis \(H_ 0\) is the complement of \(H_ 1\). A class of tests more powerful than the likelihood ratio test (LRT) is derived. Applications to two special cases, binomial and Poisson, are indicated.