Experiments have shown that adenine is most frequently incorporated opposite cis-syn cyclobutane thymine dimers and guanine is most frequently incorporated opposite cis-syn cyclobutane cytosine dimers. Specialized DNA polymerases can also misinsert guanine, thymine or cytosine nucleotides opposite the cis-syn cyclobutane thymine dimers and adenine, thymine or cytosine nucleotides opposite cis-syn cyclobutane cytosine dimers (“A-rule”). Polymerase paradigm cannot explain the incorporation of guanine, thymine or cytosine opposite cis-syn cyclobutane thymine dimers. Polymerase-tautomeric model for “A-rule” is proposed. It is based on the polymerase-tautomeric models for targeted, untargeted, targeted delayed and untargeted delayed base substitution mutagenesis. It is shown that canonical adenine can be incorporated opposite canonical cis-syn cyclobutane thymine dimers during error-prone and SOS synthesis of DNA. Canonical adenine cannot be incorporated opposite thymine in T*₁, T*₄ or T*₅ rare tautomeric forms but canonical guanine, thymine or cytosine can be incorporated during error-prone and SOS synthesis. Canonical tautomeric forms of adenine can be incorporated opposite thymine in T*₃ rare tautomeric form and canonical tautomeric forms of guanine, thymine or cytosine can be incorporated during error-prone and SOS synthesis. Molecules of thymine in T*₁, T*₃, T*₄ or T*₅ rare tautomeric forms can be part of cis-syn cyclobutane thymine dimers, and can be located in small neighborhoods from them. Canonical thymine T cannot be incorporated opposite adenine in A₁* rare tautomeric form, but canonical cytosine C or adenine A can be incorporated. Opposite adenine in А₂* rare tautomeric form thymine can be incorporated, but cytosine, guanine or adenine could be inserted. Opposite adenine in А₄* rare tautomeric form thymine can be incorporated, but guanine could be inserted. Molecules of adenine A₁*, А₂*, or А₄* can be located in small neighborhoods from cyclobutane pyrimidine dimers. Opposite thymine in canonical tautomeric form cytosine can be incorporated, and opposite adenine in canonical tautomeric form guanine could be inserted.