Estimates of genetic effective population size (Ne) using molecular markers are a potentially useful tool for the management of endangered through to commercial species. However, pitfalls are predicted when the effective size is large because estimates require large numbers of samples from wild populations for statistical validity. Our simulations showed that linkage disequilibrium estimates of Ne up to 10,000 with finite confidence limits can be achieved with sample sizes of approximately 5000. This number was deduced from empirical allele frequencies of seven polymorphic microsatellite loci in a commercially harvested fisheries species, the narrow-barred Spanish mackerel (Scomberomorus commerson). As expected, the smallest SD of Ne estimates occurred when low-frequency alleles were excluded. Additional simulations indicated that the linkage disequilibrium method was sensitive to small numbers of genotypes from cryptic species or conspecific immigrants. A correspondence analysis algorithm was developed to detect and remove outlier genotypes that could possibly be inadvertently sampled from cryptic species or nonbreeding immigrants from genetically separate populations. Simulations demonstrated the value of this approach in Spanish mackerel data. When putative immigrants were removed from the empirical data, 95% of the Ne estimates from jacknife resampling were greater than 24,000.