FINEMAP is accurate when the set of causal configurations explored captures a large majority of the total posterior probability. Our results show that this is the case in all datasets we have tested: the maximal error in any single-SNP inclusion probability is smaller than 0.11 across all 2000 datasets of Scenario B. Using exhaustive search, we observed in genomic regions with 750 SNPs of which five were truly causal that on average only the top 123 (median = 14) causal configurations out of all possible 70.3×106 already cover 95% of the total posterior probability. (Similar results were also observed for genomic regions with different numbers of SNPs.) This explains why an efficient stochastic search can achieve accurate results in a tiny fraction of the processing time of an exhaustive search. Our datasets were generated by requiring that the causal SNPs had highly correlated proxies (absolute correlation greater than 0.5) among the other variants. The high accuracy of FINEMAP throughout these tests makes us believe that FINEMAP is accurate in typical GWAS data with complex correlation structure among the SNPs.