Assembly of DNA parts into DNA constructs is a foundational technology in the emerging field of synthetic biology. An efficient DNA assembly method is particularly important for high-throughput, automated DNA assembly in biofabrication facilities and therefore we investigated one-step, scarless DNA assembly via ligase cycling reaction (LCR). LCR assembly uses single-stranded bridging oligos complementary to the ends of neighboring DNA parts, a thermostable ligase to join DNA backbones, and multiple denaturation-annealing-ligation temperature cycles to assemble complex DNA constructs. The efficiency of LCR assembly was improved ca. 4-fold using designed optimization experiments and response surface methodology. Under these optimized conditions, LCR enabled one-step assembly of up to 20 DNA parts and up to 20 kb DNA constructs with very few single-nucleotide polymorphisms (<1 per 25 kb) and insertions/deletions (<1 per 50 kb). Experimental comparison of various sequence-independent DNA assembly methods showed that circular polymerase extension cloning (CPEC) and Gibson isothermal assembly did not enable assembly of more than four DNA parts with more than 50% of clones being correct. Yeast homologous recombination and LCR both enabled reliable assembly of up to 12 DNA parts with 60-100% of individual clones being correct, but LCR assembly provides a much faster and easier workflow than yeast homologous recombination. LCR combines reliable assembly of many DNA parts via a cheap, rapid, and convenient workflow and thereby outperforms existing DNA assembly methods. LCR assembly is expected to become the method of choice for both manual and automated high-throughput assembly of DNA parts into DNA constructs.