Summary: Let a set of real numbers be divided into \(m\) disjoint intervals (cells), so that the probability that a single observation sampled from a distribution defined by a null hypothesis falls into a given cell is equal to \(1/m\). The number of empty cells is the test statistic of the David-Hellwig goodness-of-fit test. We present some results concerning the power of this test as a test of a compound normality hypothesis against some simple alternatives.