Power-divergence goodness-of-fit statistics were studied for small samples and skewed hypotheses. The accuracy of these statistics was found to depend on the smallest expected frequency, not on the skewness itself. Pearson's X2 statistic was most accurate for k > 3 and small expected frequencies, while a moment-corrected h2 distribution improved accuracy for smaller frequencies. A normal correction was effective for very small expected frequencies, ensuring accurate tests using the log-likelihood-ratio statistic G2.