Cytosine base editors (CBEs) enable programmable genomic C·G-to-T·A transition mutations and typically comprise a modified CRISPR–Cas enzyme, a naturally occurring cytidine deaminase, and an inhibitor of uracil repair. Previous studies have shown that CBEs utilizing naturally occurring cytidine deaminases may cause unguided, genome-wide cytosine deamination. While improved CBEs that decrease stochastic genome-wide off-targets have subsequently been reported, these editors can suffer from suboptimal on-target performance. Here, we report the generation and characterization of CBEs that use engineered variants of TadA (CBE-T) that enable high on-target C·G to T·A across a sequence-diverse set of genomic loci, demonstrate robust activity in primary cells and cause no detectable elevation in genome-wide mutation. Additionally, we report cytosine and adenine base editors (CABEs) catalyzing both A-to-I and C-to-U editing (CABE-Ts). Together with ABEs, CBE-Ts and CABE-Ts enable the programmable installation of all transition mutations using laboratory-evolved TadA variants with improved properties relative to previously reported CBEs.