Broadband dielectric measurements on the pharmaceutical indomethacin (IMC) were performed at ambient and elevated pressure. Data on molecular dynamics collected at ambient pressure are in good agreement with that published in the literature. In the glassy state, there is a well-resolved secondary relaxation with Arrhenius activation energy E(a) = 38 kJ/mol. This commonly observed relaxation process (labeled gamma) is of intramolecular origin because it is pressure-insensitive. Closer analysis of the ambient pressure dielectric spectra obtained in the vicinity of the T(g) indicated the presence of one more secondary relaxation (beta), which is slower than that commonly observed. Application of the CM predictions enabled us to classify it as a true JG relaxation. Pressure measurements confirmed our supposition concerning the origins of the two secondary relaxations in IMC. Moreover, we have found that IMC under pressure does not crystallize, even at very high temperatures of T > or = 372 K. This finding was discussed in the framework of the two-order parameter model proposed by Tanaka (Konishi, T.; Tanaka, H. Phys. Rev B 2007, 76, 220201), as well as the JG relaxation proposal by Oguni (Hikima T.; Hanaya M.; Oguni M. J. Mol Struct. 1999, 479, 245). We also showed that the shape of the alpha-relaxation loss peak is the same when comparing dielectric spectra with the same tau(alpha) but obtained at ambient and elevated pressure. Additionally, we found out that the fragility of IMC decreases with increasing pressure. In addition, the pressure coefficient of the glass transition temperature, dT(g)/dP, was determined, and it is 255 K/GPa. Finally, we discuss the possibility of preparation of the amorphous state with higher density than by cooling of the liquid.