The present invention encompasses engineered nucleases which recognize and cleave a recognition sequence within a Hepatitis B virus (HBV) genome. The engineered meganucleases can exhibit at least one optimized characteristic, such as enhanced specificity and/or efficiency of indel formation, when compared to the first-generation meganuclease HBV 11-12x.26. Further, the invention encompasses pharmaceutical compositions comprising engineered meganuclease proteins, nucleic acids encoding engineered meganucleases, and the use of such compositions for treating HBV infections or hepatocellular carcinoma.