  This paper discusses some problems possibly arising when approximating via
Monte-Carlo simulations the distributions of goodness-of-fit test statistics
based on the empirical distribution function. We argue that failing to
re-estimate unknown parameters on each simulated Monte-Carlo sample -- and thus
avoiding to employ this information to build the test statistic -- may lead to
wrong, overly-conservative testing. Furthermore, we present a simple example
suggesting that the impact of this possible mistake may turn out to be dramatic
and does not vanish as the sample size increases.
