We review and concurrently discuss two recent works conducted by us, which apparently give opposite results. Specifically, we have investigated how extreme thermal histories in glasses can affect their universal properties at low temperatures, by studying: (i) amber, the fossilized natural resin, which is a glass which has experienced a hyperaging process for about one hundred million years; and (ii) ultrastable thin-film glasses of indomethacin. Specific heat C-p measurements in the temperature range 0.07K < T < 30K showed that the amount of two-level systems, assessed from the linear term at the lowest temperatures, was exactly the same for the pristine hyperaged amber glass as for the subsequently rejuvenated samples, whereas just a modest increase of the boson-peak height (in C-p/T-3) with increasing rejuvenation was observed, related to a corresponding increase of the Debye coefficient. On the other hand, we have observed an unexpected suppression of the twolevel systems in the ultrastable glass of indomethacin, whereas conventionally prepared thin films of the same material exhibit the usual linear term in the specific heat below 1K ascribed to these universal two-level systems in glasses. By comparing both highly-stable kinds of glass, we conclude that the disappearance of the tunneling two-level systems in ultrastable thin films of indomethacin may be due to the quasi-2D and anisotropic behavior of this glass, what could support the idea of a phonon-mediated interaction between two-level systems. (C) 2015 AIP Publishing LLC.