Any system, natural or human-made, is better understood if we analyze both its history and its structure. Here we combine structural analyses with a "Reconstructed Evolutionary Adaptive Path" (REAP) analysis that used the evolutionary and functional history of DNA polymerases to replace amino acids to enable polymerases to accept a new class of triphosphate substrates, those having their 3'-OH ends blocked as a 3(')-ONH(2) group (dNTP-ONH(2)). Analogous to widely used 2',3'-dideoxynucleoside triphosphates (ddNTPs), dNTP-ONH(2)s terminate primer extension. Unlike ddNTPs, however, primer extension can be resumed by cleaving an O-N bond to restore an -OH group to the 3'-end of the primer. REAP combined with crystallographic analyses identified 35 sites where replacements might improve the ability of Taq to accept dNTP-ONH(2)s. A library of 93 Taq variants, each having replacements at three or four of these sites, held eight variants having improved ability to accept dNTP-ONH(2) substrates. Two of these (A597T, L616A, F667Y, E745H, and E520G, K540I, L616A) performed notably well. The second variant incorporated both dNTP-ONH(2)sand ddNTPs faithfully and efficiently, supporting extension-cleavage-extension cycles applicable in parallel sequencing and in SNP detection through competition between reversible and irreversible terminators. Dissecting these results showed that one replacement (L616A), not previously identified, allows Taq to incorporate both reversible and irreversible terminators. Modeling showed how L616A might open space behind Phe-667, allowing it to move to accommodate the larger 3'-substituent. This work provides polymerases for DNA analyses and shows how evolutionary analyses help explore relationships between structure and function in proteins.