Cytosine or adenine base editors (CBEs or ABEs) can introduce specific DNA C-to-T or A-to-G alterations^{, , –}. However, we recently demonstrated that they can also induce transcriptome-wide guide-RNA-independent editing of RNA bases, and created selective curbing of unwanted RNA editing (SECURE)-BE3 variants that have reduced unwanted RNA-editing activity. Here we describe structure-guided engineering of SECURE-ABE variants with reduced off-target RNA-editing activity and comparable on-target DNA-editing activity that are also among the smallest Streptococcus pyogenes Cas9 base editors described to date. We also tested CBEs with cytidine deaminases other than APOBEC1 and found that the human APOBEC3A-based CBE induces substantial editing of RNA bases, whereas an enhanced APOBEC3A-based CBE, human activation-induced cytidine deaminase-based CBE, and the Petromyzon marinus cytidine deaminase-based CBE Target-AID induce less editing of RNA. Finally, we found that CBEs and ABEs that exhibit RNA off-target editing activity can also self-edit their own transcripts, thereby leading to heterogeneity in base-editor coding sequences.