We explore the effects of demography and linkage on a maximum-likelihood (ML) method for estimating selection and mutation parameters in a reversible mutation model. This method assumes free recombination between sites and a randomly mating population of constant size and uses information from both polymorphic and monomorphic sites in the sample. Two likelihood-ratio test statistics were constructed under this ML framework: LRT gamma for detecting selection and LRT kappa for detecting mutational bias. By carrying out extensive simulations, we obtain the following results. When mutations are neutral and population size is constant, LRT gamma and LRT kappa follow a chi-square distribution with 1 d.f. regardless of the level of linkage, as long as the mutation rate is not very high. In addition, LRT gamma and LRT kappa are relatively insensitive to demographic effects and selection at linked sites. We find that the ML estimators of the selection and mutation parameters are usually approximately unbiased and that LRT kappa usually has good power to detect mutational bias. Finally, with a recombination rate that is typical for Drosophila, LRT gamma has good power to detect weak selection acting on synonymous sites. These results suggest that the method should be useful under many different circumstances.