ASTRAL-III is an improved version of the ASTRAL method for reconstructing species trees from gene trees, addressing the limitations of its predecessor, ASTRAL-II. ASTRAL-III significantly enhances the running time of ASTRAL-II, guaranteeing polynomial running time as a function of both the number of species (n) and the number of genes (k). It limits the bipartition constraint set (X) to grow linearly with n and k, handles polytomies more efficiently, and avoids searching parts of the search space that are mathematically guaranteed not to contain the optimal tree. The asymptotic running time of ASTRAL-III is O((nk)^{1.728}D), where D = O(nk) is the sum of degrees of all unique nodes in the input trees. Extensive simulations show that contracting low support branches in gene trees improves accuracy while reducing noise, with a threshold of 10% providing the best results. ASTRAL-III can scale up to 10,000 species and is more accurate than ASTRAL-II, making it a valuable tool for phylogenetic reconstruction.ASTRAL-III is an improved version of the ASTRAL method for reconstructing species trees from gene trees, addressing the limitations of its predecessor, ASTRAL-II. ASTRAL-III significantly enhances the running time of ASTRAL-II, guaranteeing polynomial running time as a function of both the number of species (n) and the number of genes (k). It limits the bipartition constraint set (X) to grow linearly with n and k, handles polytomies more efficiently, and avoids searching parts of the search space that are mathematically guaranteed not to contain the optimal tree. The asymptotic running time of ASTRAL-III is O((nk)^{1.728}D), where D = O(nk) is the sum of degrees of all unique nodes in the input trees. Extensive simulations show that contracting low support branches in gene trees improves accuracy while reducing noise, with a threshold of 10% providing the best results. ASTRAL-III can scale up to 10,000 species and is more accurate than ASTRAL-II, making it a valuable tool for phylogenetic reconstruction.