Duplex sequencing was originally developed to detect rare nucleotide polymorphisms normally obscured by the noise of high-throughput sequencing. Here we describe a new, streamlined, reference-free approach for the analysis of duplex sequencing data. We show the approach performs well on simulated data and precisely reproduces previously published results and apply it to a newly produced dataset, enabling us to type low-frequency variants in human mitochondrial DNA. Finally, we provide all necessary tools as stand-alone components as well as integrate them into the Galaxy platform. All analyses performed in this manuscript can be repeated exactly as described at http://usegalaxy.org/duplex.