Knowing the amount of DNA polymorphism is essential to understand the mechanism of maintaining DNA polymorphism in a natural population. The amount of DNA polymorphism can be measured by the average number of nucleotide differences per site (pi), the proportion of segregating (polymorphic) site (s) and the minimum number of mutations per site (s*). Since the latter two quantities depend on the sample size, theta is often used as a measure of the amount of DNA polymorphism, where theta = 4Nmu, N is the effective population size and mu is the neutral mutation rate per site per generation. It is known that theta estimated from pi, s and s* under the infinite site model can be biased when the mutation rate varies among sites. We have therefore developed new methods for estimating theta under the finite site model. Using computer simulations, it has been shown that the new methods give almost unbiased estimates even when the mutation rate varies among sites substantially. Furthermore, we have also developed new statistics for testing neutrality by modifying Tajima's D statistic. Computer simulations suggest that the new test statistics can be used even when the mutation rate varies among sites.