Three-quanta positron annihilation can be a useful chemical probe. 3γ yields have so far been inferred from subtle changes in the gamma spectra. Peak-valley analysis, a method for quantifying 3γ yields, is susceptible to changes in the gamma spectra due not to three-quanta events but to confounding factors such as photon scatter. Based on FLUKA simulations, this work examines its validity and limitation, and proposes an optimized setup. Findings and discussions will be supported by a selection of annotated sample histories, presented interaction by interaction, from Monte Carlo simulations.