This paper compares and investigates the generalised Neyman smooth test, its components, and the classical chi-squared test with a variety of equiprobable classes. Each test is evaluated in terms of its power to reject a wavelike alternative to the uniform distribution, chosen to quantify the complexity of the alternative. Results indicate that if broadly focused tests (rather than strongly directional or weakly omnibus) are sought, then smooth tests of order about four, or the chi-squared test with between five and ten classes, will perform well.