The genetic contribution to DNA methylation has been studied through identifying methylation quantitative trait loci (mQTL). A trivial example of an mQTL is a SNP at the CpG site (CpG-SNP) which will change the C or G in the CpG sequence, and consequently the DNA methylation. Such sites have a known causal variant with a large effect and thus are potential model traits to test fine-mapping methodology. Using DNA methylation data from the Lothian Birth Cohorts of 1921 and 1936 (n=1366), we compare two methods never previously used for fine-mapping (the J-test and BSLMM) with the widely used BIMBAM method by constructing a 95% credible set of causal SNPs for mQTL with a CpG-SNP. All three methods failed to capture the CpG-SNP with the expected 95% probability. Simulations confirmed the three methods performed as expected under ideal conditions. The influence of multiple, independent signals underlying the mQTL was also excluded. Comparing the CpG-SNP, and the most associated SNP (top-SNP), we found that often the effect of the top-SNP was masking the effect of the CpG-SNP. This was shown to be more evident in CpG islands, where the fine-mapping methods captured the CpG-SNP less often than in non-island regions (OR=1.6, p=2×10-3). This indicates that methylation sites within a CpG island and the surrounding region can share common genetic control, providing potential insight into the mechanisms underlying the maintenance of DNA methylation at CpG islands.