Species are fundamental units in studies of systematics, biodiversity and ecology, but their delimitation has been relatively neglected methodologically. Species are typically circumscribed based on the presence of fixed (intraspecifically invariant or non-overlapping) diagnostic morphological characters which distinguish them from other species. In this paper, we argue that determining whether diagnostic characters are truly fixed with certainty is generally impossible with finite sample sizes and we show that sample sizes of hundreds or thousands of individuals may be necessary to have a reasonable probability of detecting polymorphisms in diagnostic characters at frequencies approaching zero. Instead, we suggest that using a non-zero frequency cut-off may be a more realistic and practical criterion for character-based species delimitation (for example, allowing polymorphisms in the diagnostic characters at frequencies of 5% or less). Given this argument, we then present a simple statistical method to evaluate whether at least one of a set of apparently diagnostic characters is below the frequency cut-off. This method allows testing of the strength of the evidence for species distinctness and is readily applicable to empirical studies.