We investigate alternative strategies against reference bias and postmortem damage in low coverage paleogenomes. Compared to alignment to the linear reference genome, we show that masking known polymorphic sites and graph alignment effectively remove reference bias, but only starting from raw read files. We next study approaches to overcome postmortem damage: trimming, rescaling, and our newly developed algorithm, bamRefine (github.com/etkayapar/bamRefine and zenodo.org/records/14234666), masking reads only at positions possibly affected by PMD. We propose graph alignment coupled with bamRefine as a simple strategy to minimize data loss and bias, and urge the community to publish FASTQ files.