We show thatin silicodesign of DNA secondary structures is improved by extending the base pairing alphabet beyond A-T and G-C to include the pair between 2-amino-8-(1'-β-D-2'-deoxyribofuranosyl)-imidazo-[1,2-a]-1,3,5-triazin-(8H)-4-one and 6-amino-3-(1'-β-D-2'-deoxyribofuranosyl)-5-nitro-(1H)-pyridin-2-one, simply P and Z. To obtain the thermodynamic parameters needed to include P-Z pairs in the designs, we performed 47 optical melting experiments and combined the results with previous work to fit a new set of free energy and enthalpy nearest neighbor folding parameters for P-Z pairs and G-Z wobble pairs. We find that G-Z pairs have stability comparable to A-T pairs and therefore should be considered quantitatively by structure prediction and design algorithms. Additionally, we extrapolated the set of loop, terminal mismatch, and dangling end parameters to include P and Z nucleotides. These parameters were incorporated into the RNAstructure software package for secondary structure prediction and analysis. Using the RNAstructure Design program, we solved 99 of the 100 design problems posed by Eterna using the ACGT alphabet or supplementing with P-Z pairs. Extending the alphabet reduced the propensity of sequences to fold into off-target structures, as evaluated by the normalized ensemble defect (NED). The NED values were improved relative to those from the Eterna example solutions in 91 of 99 cases where Eterna-player solutions were provided. P-Z-containing designs had average NED values of 0.040, significantly below the 0.074 of standard-DNA-only designs, and inclusion of the P-Z pairs decreased the time needed to converge on a design. This work provides a sample pipeline for inclusion of any expanded alphabet nucleotides into prediction and design workflows.