Adenine base editors (ABEs) enable precise and efficient conversion of target A•T base pairs to G•C base pairs in genomic DNA with a minimum of by-products. While ABEs have been reported to exhibit minimal off-target DNA editing, off-target editing of cellular RNA by ABEs has not been examined in depth. Here, we demonstrate that a current ABE generates low but detectable levels of widespread adenosine-to-inosine editing in cellular RNAs. Using structure-guided principles to design mutations in both deaminase domains, we developed new ABE variants that retain their ability to edit DNA efficiently but show greatly reduced RNA editing activity, as well as lower off-target DNA editing activity and reduced indel by-product formation, in three mammalian cell lines. By decoupling DNA and RNA editing activities, these ABE variants increase the precision of adenine base editing by minimizing both RNA and DNA off-target editing activity.