The bias energies of various two-level systems (TLSs) and their strengths of interactions with the strain are calculated for Ar:N2 glass. Unlike the case in KBr:CN, a distinct class of TLSs having weak interaction with the strain and untypically small bias energies is not found. The addition of CO molecules introduces CO flips which form such a class of weakly interacting TLSs, albeit at much lower coupling than that at which they are typically observed in solids. We conclude that because of the absence of a distinct class of weakly interacting TLSs, Ar:N2 is a non-universal glass, the first such system in three dimensions and in ambient pressure. Our results further suggest that Ar:N2:CO may show universal properties, but at temperatures lower than , much smaller than the typical temperature associated with universality, because of the untypical softness of this system. Our results thus shed light on two long-standing questions regarding the low-temperature properties of glasses: the necessary and sufficient conditions for quantitative universality of phonon attenuation, and what dictates the energy scale of ≈ 3 K below which universality is typically observed.