Exogenous DNA can be a template to precisely edit a cell's genome. However, the delivery of in vitro-produced DNA to target cells can be inefficient, and low abundance of template DNA may underlie the low rate of precise editing. One potential tool to produce template DNA inside cells is a retron, a bacterial retroelement involved in phage defense. However, little effort has been directed at optimizing retrons to produce designed sequences. Here, we identify modifications to the retron non-coding RNA (ncRNA) that result in more abundant reverse-transcribed DNA (RT-DNA). By testing architectures of the retron operon that enable efficient reverse transcription, we find that gains in DNA production are portable from prokaryotic to eukaryotic cells and result in more efficient genome editing. Finally, we show that retron RT-DNA can be used to precisely edit cultured human cells. These experiments provide a general framework to produce DNA using retrons for genome modification.