The problem of deriving reliable tests for separate families of hypotheses is discussed. Two competing methodologies for testing hypotheses from separate distributional families, the classical asymptotic approach of Cox [1961,1962] and more modern methods using Monte Carlo or parametric bootstrap simulation, are contrasted. It is shown that the two methods can be combined to form a test with excellent statistical properties. Variants of simulation-based tests are discussed. In addition, simple computational strategies using parallel computers are described that can be used to reduce the combined test's heavy simulation load.