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[en] Photovoltaic conversion efficiencies of 32.6 +/- 1.4% under the AM1.5 G173 global spectrum, and 35.5 +/- 1.2% at 38-suns concentration under the direct spectrum, are demonstrated for a monolithic, dual-junction 1.7/1.1 eV solar cell. The tandem cell consists of a 1.7 eV GaInAsP top-junction grown lattice-matched to a GaAs substrate, followed by a metamorphic 1.1 eV GaInAs junction grown on a transparent, compositionally graded metamorphic AlGaInAs buffer. This bandgap combination is much closer to the dual-junction optimum and offers headroom for absolute 3% improvement in efficiency, in comparison to the incumbent lattice-matched GaInP/GaAs (~1.86/1.41 eV) solar cells. The challenge of growing a high-quality 1.7 eV GaInAsP solar cell is the propensity for phase separation in the GaInAsP alloy. The challenge of lattice-mismatched GaInAs solar cell growth is that it requires minimizing the residual dislocation density during the growth of a transparent compositionally graded buffer to enable efficient metamorphic tandem cell integration. Transmission electron microscopy reveals relatively weak composition fluctuation present in the 1.7 eV GaInAsP alloy, attained through growth control. The threading dislocation density of the GaInAs junction is ~1 x 10^6 cm-2, as determined from cathodoluminescence measurements, highlighting the quality of the graded buffer. These material advances have enabled the performance of both junctions to reach over 80% of their Shockley-Queisser limiting efficiencies, with both the subcells demonstrating a bandgap-voltage offset, WOC (=Eg/q-VOC), of ~0.39 V.