The potential benefits of using population isolates in genetic mapping, such as reduced genetic, phenotypic and environmental heterogeneity, are offset by the challenges posed by the large amounts of direct and cryptic relatedness in these populations confounding basic assumptions of independence. We have evaluated four representative specialized methods for association testing in the presence of relatedness; (i) within-family (ii) within- and between-family and (iii) mixed-models methods, using simulated traits for 2906 subjects with known genome-wide genotype data from an extremely isolated population, the Island of Kosrae, Federated States of Micronesia. We report that mixed models optimally extract association information from such samples, demonstrating 88% power to rank the true variant as among the top 10 genome-wide with 56% achieving genome-wide significance, a >80% improvement over the other methods, and demonstrate that population isolates have similar power to non-isolate populations for observing variants of known effects. We then used the mixed-model method to reanalyze data for 17 published phenotypes relating to metabolic traits and electrocardiographic measures, along with another 8 previously unreported. We replicate nine genome-wide significant associations with known loci of plasma cholesterol, high-density lipoprotein, low-density lipoprotein, triglycerides, thyroid stimulating hormone, homocysteine, C-reactive protein and uric acid, with only one detected in the previous analysis of the same traits. Further, we leveraged shared identity-by-descent genetic segments in the region of the uric acid locus to fine-map the signal, refining the known locus by a factor of 4. Finally, we report a novel associations for height (rs17629022, P< 2.1 × 10⁻⁸).