We characterized stacked double-pyramidal quantum dots which showed biexciton binding energies close to zero by means of photoluminescence and cross-correlation measurements. It was possible to obtain a sequence of two photons with (nearly) the same energy from the biexciton-exciton-ground state cascade, as corroborated by a basic rate-equation model. This type of two-photon emission is both of relevance for fundamental quantum information theory studies as well as for more exotic applicative fields such as quantum biology.