Recently described base editor (BE) technology, which uses CRISPR-Cas9 to direct cytidine deaminase enzymatic activity to specific genomic loci, enables the highly efficient introduction of precise cytidine-to-thymidine (C to T) DNA alterations in many different cell types and organisms. In contrast to genome-editing nucleases, BEs avoid the need to introduce double-strand breaks or exogenous donor DNA templates and induce lower levels of unwanted variable-length insertion/deletion mutations (indels). However, existing BEs can also efficiently create unwanted C to T alterations when more than one C is present within the five base pair "editing window" of these proteins, a lack of precision that can cause potentially deleterious bystander mutations. Mutations in the cytidine deaminase enzyme can shorten the length of the editing window and thereby partially address this limitation but these BE variants still do not discriminate among multiple cytidines within the narrowed window and also possess a more limited targeting range. Here, we describe an alternative strategy for reducing bystander mutations using a novel BE architecture that harbors an engineered human APOBEC3A (eA3A) domain, which preferentially deaminates cytidines according to a TCR>TCY>VCN (V = G, A, C, Y = C, T) hierarchy. In direct comparisons with the widely used BE3 fusion in human cells, our eA3A-BE3 fusion exhibits comparable activities on cytidines in TC motifs but greatly reduced or no significant editing on cytidines in other sequence contexts. Importantly, we show that eA3A-BE3 can correct a human beta-thalassemia promoter mutation with much higher (>40-fold) precision than BE3, substantially minimizing the creation of an undesirable bystander mutation. Surprisingly, we also found that eA3A-BE3 shows reduced mutation frequencies on known off-target sites of BE3, even when targeting promiscuous homopolymeric sites. Our results validate a general strategy to improve the precision of base editors by engineering their cytidine deaminases to possess greater sequence specificity, an important proof-of-principle that should motivate the development of a larger suite of new base editors with such properties.