  The existence of a constant density of two-level systems (TLS) was proposed
as the basis of some intriguing universal aspects of glasses at ultra-low
temperatures. Here we ask whether their existence is necessary for explaining
the universal density of states quasi-localized modes (QLM) in glasses at
ultra-low temperatures. A careful examination of the QLM that exist in a
generic atomistic model of a glass former reveals at least two types of them,
each exhibiting a different density of states, one depending on the frequency
as $\omega^3$ and the other as $\omega^4$. The properties of the glassy energy
landscape that is responsible for the two types of modes is examined here,
explaining the analytic feature responsible for the creations of (at least) two
families of QLM's. Although adjacent wells certainly exist in the complex
energy landscape of glasses, doubt is cast on the relevance of TLS for the
universal density of QLM's.
