Rapid improvements in DNA sequencing technology have resulted in long genome sequences for a large number of similar isolates with a wide range of single nucleotide polymorphism (SNP) rates, where some isolates can have thousands of times lower SNP rates than others. Genome sequences of this kind are a challenge to existing methods for construction of phylogenetic trees. We address the issues by developing a hierarchical approach to phylogeny construction. In this method, the construction is performed at multiple levels, where at each level, groups of isolates with similar levels of similarity are identified and their phylogenetic trees are constructed. Time savings are achieved by using a sufficiently large number of columns from the input alignment, instead of all its columns. Our results show that the new approach is 20-60 times more efficient than existing programs and more accurate in situations where highly similar isolates have a wide range of SNP rates.