Positron annihilation methods concentrate on 2γ-annihilation, even though 3γ-annihilation often plays a considerable role. Distortions introduced by the time resolution-optimizing selection of narrow energy windows (taking only the upper part of the energy spectrum of the stop signals) in positron lifetime spectroscopy employing fast plastic scintillators and by analyzing the 0.511 MeV region alone in the Doppler-effect measurements were investigated here. Positron data collected for materials with Ps-hosting features (fine powders of MgO, Al2O3, SiO2 and zeolites) will be discussed from these aspects. It was found that the long lifetimes and their intensities may well differ in dependence on the energy settings. Significant differences found in the energy spectra of the annihilation radiation for 2γ- and 3γ- annihilation were also analyzed determining the respective statistical utility rates.