GaAs is often used as a multijunction subcell due to its high material quality on GaAs substrates, despite having a non-optimal bandgap. The bandgap can be beneficially reduced using many layers of thin, strain-balanced GaInAs in a superlattice or quantum well device, but achieving excellent carrier collection without increased recombination has proven challenging. Here, we develop and demonstrate high performance, optically thick GaInAs/GaAsP strain-balanced solar cells. Excellent material quality is achieved in thick superlattices by using growth conditions that limit progressive thickness and composition fluctuations. Bandgap-voltage offsets as low as 0.31 V are shown in superlattice cells using thin, highly strained GaP barriers. Optically thick superlattice cells with over 2500 nm of total GaInAs in the depletion region are developed, enabling 3.8 mA/cm2 of extra photocurrent beyond the GaAs band edge under the AM0 space spectrum. Optimized superlattice solar cells are incorporated into two-junction devices that achieve 29.2% efficiency under the AM0 space spectrum due to their improved bandgap combination and high subcell voltages.