Although the extreme tails of the distributions of equity returns tend to exhibit more negative than positive returns, very few studies have analysed how pervasive is skewness across entire distributions. We use daily returns on 6 international stock market indices from Britain, France, Germany, Italy, Japan and the United States over 24 years from January 1978 to February 2002 to search for skewness in the tails, in different intervals, and in the entire distributions using binomial distribution tests and two distribution free tests, the Wilcoxon Rank Sum Test and the Siegel-Tukey test. We find limited evidence of asymmetry in the tails, with more asymmetry close to the means. However, we find that the asymmetries closer to the means are statistically significant and consistent in a way that the asymmetry in the tails is not. We show via a Monte Carlo study that the Wilcoxon Rank Sum and Binomial Distribution test have good power inferring that the data are independent and identically distributed.