We present a pulsational stability analysis of hot post-asymptotic giant branch (AGB) H-deficient pre-white dwarf stars with active He-burning shells. The stellar models employed are state-of-the-art equilibrium structures representative of PG1159 stars derived from the complete evolution of the progenitor stars, through the thermally pulsing AGB phase and born-again episode. On the basis of fully nonadiabatic pulsation computations, we confirmed theoretical evidence for the existence of a separate PG1159 instability strip in the log T eff-log g diagram characterized by short-period g-modes excited by the epsilon-mechanism. This instability strip partially overlaps the already known GW Vir instability strip of intermediate/long-period g-modes destabilized by the classical κ-mechanism acting on the partial ionization of C and/or O in the envelope of PG1159 stars. We found that PG1159 stars characterized by thick He-rich envelopes and located inside this overlapping region could exhibit both short and intermediate/long periods simultaneously. As a natural application of our results, we study the particular case of VV 47, a pulsating planetary nebula nucleus (PG1159 type) that is particularly interesting because it has been reported to exhibit a rich and complex pulsation spectrum including a series of unusually short pulsation periods. We found that the long periods exhibited by VV 47 can be readily explained by the classical κ-mechanism, while the observed short-period branch below ≈300 s could correspond to modes triggered by the He-burning shell through the epsilon-mechanism, although more observational work is needed to confirm the reality of these short-period modes. Were the existence of short-period g-modes in this star convincingly confirmed by future observations, VV 47 could be the first known pulsating star in which both the κ-mechanism and the epsilon-mechanism of mode driving are simultaneously operating.