In yeast, the pol3-01,L612M double mutant allele, which causes defects in DNA polymerase delta (Pol δ) proofreading (pol3-01) and nucleotide selectivity (pol3-L612M), confers an "ultramutator" phenotype that rapidly drives extinction of haploid and diploid MMR-proficient cells. Here, we investigate antimutator mutations that encode amino acid substitutions in Pol δ that suppress this lethal phenotype. We find that most of the antimutator mutations individually suppress the pol3-01 and pol3-L612M mutator phenotypes. The locations of many of the amino acid substitutions in Pol δ resemble those of previously identified antimutator substitutions; however, two novel mutations encode substitutions (R674G and Q697R) of amino acids in the fingers domain that coordinate the incoming dNTP. These mutations are lethal without pol3-L612M and markedly change the mutation spectra produced by the pol3-01,L612M mutator allele, suggesting that they alter nucleotide selection to offset the pol3-L612M mutator phenotype. Consistent with this hypothesis, mutations and drug treatments that perturb dNTP pool levels disproportionately influence the viability of pol3-L612M,R674G and pol3-L612M,Q697R cells. Taken together, our findings suggest that mutation rate can evolve through genetic changes that alter the balance of dNTP binding and dissociation from DNA polymerases.