In the context of structure-preserving schemes for turbulent simulations, a desirable property for numerical discretizations of the compressible Euler equations is that of being Pressure Equilibrium Preserving (PEP) (Shima et al., 2021), i.e., if pressure and velocity distributions are initially constant, as found at contact interfaces, they should remain constant even with varying density. This paper presents an analysis of existing PEP schemes and of the necessary conditions for achieving the PEP property in compressible flow simulations of ideal gas. From this, strategies are derived to modify existing schemes and impart them with the PEP property. For example, classical schemes with numerical fluxes based on the arithmetic mean of the energy (e.g. Pirozzoli, 2010 and Kuya et al., 2018) can be made PEP through the use of the harmonic mean. This mean has been recently introduced for the construction of PEP and Asymptotically Entropy-Conservative (AEC) schemes DeMichele and Coppola 2023. The effectiveness of the proposed schemes is validated on classical test cases.